NCERT Solutions for Class 12 Maths Chapter 10 – Vector Algebra Ex 10.3
Page No 447:
Question 1:
Find the angle between two vectors
and
with magnitudes
and 2, respectively having
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m632093a2.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m43090a75.gif)
Answer:
It is given that,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_214d5185.gif)
Now, we know that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_mf1b0571.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_mb8a21db.gif)
Hence, the angle between the given vectors
and
is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7532/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_me8702c8.gif)
Question 2:
Find the angle between the vectors![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m2a73fa3b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m2a73fa3b.gif)
Answer:
The given vectors are![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m76136a67.gif)
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m76136a67.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_29efb5d3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m4dbfe4b1.gif)
Also, we know that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_mf1b0571.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7534/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_1512d95c.gif)
Question 3:
Find the projection of the vector
on the vector
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_ea7cafc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_38ac4c8d.gif)
Answer:
Let
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4afe7e30.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m7d41da06.gif)
Now, projection of vector
on
is given by,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6fdf296d.gif)
Hence, the projection of vector
on
is 0.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7537/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
Question 4:
Find the projection of the vector
on the vector
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_2ab98962.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_405023ae.gif)
Answer:
Let
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m555eae67.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_3b30b389.gif)
Now, projection of vector
on
is given by,
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7539/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_73c36607.gif)
Question 5:
Show that each of the given three vectors is a unit vector:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7541/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m32f48e2.gif)
Also, show that they are mutually perpendicular to each other.
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7541/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m7fb0ff16.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7541/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m5a1cfb7b.gif)
Thus, each of the given three vectors is a unit vector.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7541/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6e28f8a3.gif)
Hence, the given three vectors are mutually perpendicular to each other.
Page No 448:
Question 6:
Find
and
, if
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7542/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_67ece5bd.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7542/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m6b122e6d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7542/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m1a0456a7.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7542/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m328a8463.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7542/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_53bef817.gif)
Question 7:
Evaluate the product
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7545/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m4e11d13d.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7545/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m406f2182.gif)
Question 8:
Find the magnitude of two vectors
, having the same magnitude and such that the angle between them is 60° and their scalar product is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_469c0fd8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_eeecab0.gif)
Answer:
Let θ be the angle between the vectors![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m5efc2d7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m5efc2d7.gif)
It is given that![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m65321064.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m65321064.gif)
We know that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_mf1b0571.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7546/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_75f3a533.gif)
Question 9:
Find
, if for a unit vector
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7548/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_711b7d68.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7548/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_439330b0.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7548/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_7454bbb6.gif)
Question 10:
If
are such that
is perpendicular to
, then find the value of λ.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7550/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_9849d88.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7550/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m27c8212b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7550/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m66b53561.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7550/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m4b5ff0c9.gif)
Hence, the required value of λ is 8.
Question 11:
Show that
is perpendicular to
, for any two nonzero vectors![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_469c0fd8.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m780e99e3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m6f876ccf.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_469c0fd8.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m1a082f75.gif)
Hence,
and
are perpendicular to each other.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m780e99e3.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7551/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m6f876ccf.gif)
Question 12:
If
, then what can be concluded about the vector
?
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_1df65f0a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
Answer:
It is given that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_1df65f0a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_abe8c8c.gif)
Hence, vector
satisfying
can be any vector.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6d43734a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7553/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m22ea9a3a.gif)
Question 13:
If
are unit vectors such that
, find the value of
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_76ff205a.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_26fcd885.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_5667a68.gif)
Answer:
It is given that
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_26fcd885.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_59d46152.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_m402f0cef.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_1171f589.gif)
From (1), (2) and (3),
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/1/239/12590/CBSE%20Math%20Grade%2012_Missing%20solution_html_m42dd0c9d.gif)
Question 14:
If either vector
, then
. But the converse need not be true. Justify your answer with an example.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7555/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_218a65fa.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7555/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m22ea9a3a.gif)
Answer:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7555/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m484e322c.gif)
We now observe that:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7555/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_19238cb7.gif)
Hence, the converse of the given statement need not be true.
Question 15:
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors
and
]
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m63957436.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_2fb90e8e.gif)
Answer:
The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).
Also, it is given that ∠ABC is the angle between the vectors
and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m63957436.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_2fb90e8e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m55a3c420.gif)
Now, it is known that:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m34a9cefc.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7556/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m78f7f6f4.gif)
Question 16:
Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
Answer:
The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7558/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_6128d1c9.gif)
Hence, the given points A, B, and C are collinear.
Question 17:
Show that the vectors
form the vertices of a right angled triangle.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7560/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_1f753d06.gif)
Answer:
Let vectors
be position vectors of points A, B, and C respectively.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7560/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_1f753d06.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7560/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m6b0b8e58.gif)
Now, vectors
represent the sides of ΔABC.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7560/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_7ee52a46.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7560/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m33c493f8.gif)
Hence, ΔABC is a right-angled triangle.
Question 18:
If
is a nonzero vector of magnitude ‘a’ and λ a nonzero scalar, then λ
is unit vector if
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_4f2bfef5.gif)
(A) λ = 1 (B) λ = –1 (C) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m659bfefb.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m659bfefb.gif)
(D) ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_10bae266.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_10bae266.gif)
Answer:
Vector
is a unit vector if
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m4d5ff0d7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m5dc91ba9.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m1e63fb7.gif)
Hence, vector
is a unit vector if
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_m4d5ff0d7.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/239/7561/NCERT_10-11-08_Khushboo_12_Math_Ex-10.1_5.doc_SG_html_10bae266.gif)
The correct answer is D.