CBSE Class 12 Maths Chapter-10 Important Questions – Free PDF Download
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CBSE Class 12 Mathematics Important Questions Chapter 10 – Vector Algebra
1 Mark Questions
1. Is the measure of 5 seconds is scalar or vector?
Ans: Scalar
2. Find the sum of the vectors.
Ans: 
3. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 
D.C of 
4. Find the angle between vectors 
Ans: 
5. Vectors 
be such that 
then 
is a unit vector. Find angle between.
Ans: 
6. Is the measure of 10 Newton is scalar or vector.
Ans:Vector
7. Write two different vectors having same magnitude.
Ans: 
8. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 
9. Find 
Ans:
10. If 
Ans: 
11. Is the measure of 20 m/s towards north is scalar or vector.
Ans: Vector
12. 
Ans: 
13. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 
D.C of 
14. Evaluate the product 
Ans:
15. Find if 
Ans: 
16. Is the measure of 30 m/s towards north is scalar or vector.
Ans: Scalar
17. Compute the magnitude of
Ans: 
18. Find the direction ratios and the direction cosines of the vector 
Ans: D.R of 
D.C of 
19. 
Is unit vector and 
Then find 
Ans:
20. Show that 
Ans: 
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4 Mark Questions
1. Find the unit vector in the direction of the sum of the vectors 
Ans: Let 
The required unit vector is
2. Show that the points 
are the vertices of right angled triangle.
Ans: 
Hence, the 
is a right angled triangle.
3. Show that the points 
are collinear.
Ans: 
Hence points A, B, C are collinear.
4. If 
are unit vector such that 
find the value of 
Ans: 
5. If 
are such that 
is then find the value of
.
Ans: 
6. Consider two point P and Q with position vectors
. Find the positions vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally (ii) externally.
Ans: (i) 
(ii) 
7. Show that the points A, B, C with position vectors 
respectively are collinear.
Ans: 
Thus 
but one point B is common to both vectors hence A, B, C are collinear.
8. Find a unit vector 
to each of the vectors 
Ans: A vector which is to both 
is giving by
Req. unit vector is
9. The scalar product of the vector 
with a unit vector along the sum of vectors 
is equal the one. Find the value of
Ans: 
Unit vector along
10. Find the area of the with vertices A (1, 1, 2) B (2, 3, 4) and C (1, 5, 5).
Ans: A (1, 1, 2) B(2, 3, 4) C (1, 5, 5)
OB¯¯¯¯¯¯¯¯=2i^+3j^+4k^OB¯=2i^+3j^+4k^
OC¯¯¯¯¯¯¯¯=i^+5j^+5k^OC¯=i^+5j^+5k^
11. Show that the points A (1, -2, -8) B (5, 0, -2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
Ans:A (1, -2, -8), B (5, 0, -2), C (11, 3, 7)
Thus 
and one point B is common there fore A, B, C are collinear and B divides AC in 2:3.
12. Find a vector 
which is 
to both 
and 
and 
.=15
Let 
Ans:
On solving equation (i) and (ii)
Put x, y, z in equation (iii)
13. Let 
be three vectors such that 
and each one of them being to the sum of the other two, find 
Ans: 
14. If 
Find the angel between the vectors 
Ans: 
15. Find the sine of the angel between the vectors.
Ans: 
16. Three vectors satisfy the condition Evaluate the quantity 
if 
Ans:
Adding (i) (ii) and (iii)
17. If with reference to the right handed system of mutually unit vectors 
then express 
in the form
, where 
is || to 
and 
isto
Ans: 
18. If be three vectors such that and 
find the angle between 
Ans:
19. Find the area of the ||gm whose adjacent sides are represented by the vectors, 
Ans: 
20. Find the vector joining the points P (2, 3, 0) and Q (-1, -2, -4) directed from P to Q. Also find direction ratio and direction cosine.
Ans: 
