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Install NowNCERT Solutions class 12 Maths Exercise 10.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.
Download NCERT solutions for Vector Algebra as PDF.
NCERT Solutions class 12 Maths Vector Algebra
1. Compute the magnitude of the following vectors:
Ans. Given: 
And 
Also 
2. Write two different vectors having same magnitude.
Ans. Let and 
Clearly, 
[
Coefficients of 
and 
are same in vectors 
and 
coefficients of 
in and are unequal as 
]
But
And 
3. Write two different vectors having same direction.
Ans. Let 
and 
= 
where 
= 2 > 0
Vectors and have the same direction.
But 
4. Find the values of 
and 
so that the vectors 
and 
are equal.
Ans. Given: 
Comparing coefficients of and on both sides, we have,
and 
5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point 
Ans. Let 
be the vector with initial point A (2, 1) and terminal point B
Position vector of point A is (2, 1) = 
and position vector of point B is 
= 
= Position vector of point B – Position vector of point A
= 
= 
= 
Scalar components of the vectors are coefficients of and in i.e., 
and 6 and vector components of the vector are 
and 
6. Find the sum of the vectors: 
and 
Ans. Given: 
and
Adding, 
= 
7. Find the unit vector in the direction of the vector 
Ans. We know that a unit vector in the direction of the vector 
is
8. Find the unit vector in the direction of the vector 
where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.
Ans. Given: Points P (1, 2, 3) and Q (4, 5, 6)
Position vector of point P = 
= 
and position vector of Q = 
= 
, where O is the origin.
= Position vector of Q – Position vector of P = 
= 
= 
Therefore, the unit vector in the direction of vector = 
= 
= 
9. For given vectors 
and 
find the unit vector in the direction of 
Ans. Given: Vectors and 
= 
10. Find the vector in the direction of vector 
which has magnitude 8 units.
Ans. Let 
A vector in the direction of vector which has magnitude 8 units = 
= 
= 
= 
11. Show that the vectors 
and 
are collinear.
Ans. Let 
and 
= 
= 
= 
where 
12. Find the direction cosines of the vector 
Ans. The given vector is 
= 
We know that the direction cosines of a vector are coefficients of 
in i.e., 
13. Find the direction cosines of the vector joining the points A
and B
directed from A to B.
Ans. Given: Points A and B
Position vector of point A = 
= 
And Position vector of point B = 
= 
Vector = = 
= 
Now 
= 
A unit vector along 
= 
Therefore, the direction cosines of vector = 
14. Show that the vector 
is equally inclined to the axes OX, OY and OZ.
Ans. Let
Let us find angle 
(say) between vector and OX 
= 
= 
Similarly angle 
(say) between vector and OY 
is 
And angle 
(say) between vector and OZ 
is
= =
Vector is equally inclined to OX, OY and OZ.
15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are 
and 
respectively, in the ratio 2 : 1 (i) internally (ii) externally.
Ans. Position vector of P is 
and Position vector of Q is 
(i) Position vector of point R dividing PQ internally (i.e., R lies within the segment PQ) in the ratio 2 : 1 = 
= PR : QR is 
= 
= 
(ii) Position vector of point R dividing PQ externally (i.e., R lies outside the segment PQ and to the right of point Q because ratio 2 : 1 > 1 i.e., PR : QR = 2 : 1) is 
= 
= 
NCERT Solutions class 12 Maths Exercise 10.2
16. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q
Ans. Given: Point P (2, 3, 4) and Q
Position vector of point P is 
And Position vector of point Q is 
And Position vector of mid-point R of PQ is 
= 
= 
NCERT Solutions class 12 Maths Exercise 10.2
17. Show that the points A, B and C with position vectors 
and 
respectively form the vertices of a right angled triangle.
Ans. Given: Position vector of point A is 
Position vector of point B is 
and
Position vector of point C is 
where O is the origin.
Now = Position vector of point B – Position vector of point A
= 
= 
= 
……….(i)
= Position vector of point C – Position vector of point B
= 
= 
= 
……….(ii)
= Position vector of point C – Position vector of point A
= 
= 
= 
……….(iii)
Adding eq. (i) and (ii),
+ = = = [By eq. (iii)]
Now From eq. (i),AB = 
From eq. (ii),BC = 
From eq. (iii),AC = 
Here, we can observe that (Longest side BC)2 = 
AB2 + AC2
Therefore, A B, C are the vertices of a right angled triangle.
NCERT Solutions class 12 Maths Exercise 10.2
18. In triangle ABC (Fig. below), which of the following is not true:
(A) 
(B) 
(C) 
Ans. We know by Triangle law of Addition of vectors that 
Therefore option (C) is not true because in option (C),
NCERT Solutions class 12 Maths Exercise 10.2
19. If and are two collinear vectors, then which of the following are incorrect:
(A) = 
for some scalar 
(B) 
(C) The respective components of and are proportional.
(D) Both the vectors and have same direction, but different magnitudes.
Ans. Option (D) is not true because two collinear vectors can have different directions and also different magnitudes.
The option (A) and option (C) are true by definition of collinear vectors.
Option (B) is a particular case of option (A) taking 
NCERT Solutions class 12 Maths Exercise 10.2
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