MULTIPLE CHOICE QUESTIONS CHAPTER – 10 10 VECTOR ALGEBRA Q1. If a and b are the vectors forming consecutive sides of a regular hexagon ABCDEF ABCDEF , then the vector
representing the side CD is: (a) a b
(d) a b
(c) b a
(b) a b
Q2. The vector cos cos i cos sin j sin k is a: ˆ
(a) null vector
ˆ
ˆ
(b) unit vector
(c) contant vector
(d) none of these
Q3. The vector in the direction of the vector a i 2 j 2k that has a magnitude 9 is: ˆ
(a) i 2 j 2k ˆ
ˆ
ˆ
(b)
1
i 2 j 2k 3 ˆ
ˆ
ˆ
ˆ
(c) 3 i 2 j 2k
ˆ
ˆ
ˆ
ˆ
(d) 9 i 2 j 2k ˆ
ˆ
ˆ
Q4. The projection of the vector a 3i j 2k on b i 2 j 3k is: ˆ
(a)
14 2
(b) 14
ˆ
ˆ
ˆ
2
(c)
ˆ
ˆ
14
(d) 7
Q5. The p.v.’s of the points A , B , C are 2i j k , 3i 2 j k and i 4 j 3k respectively. These points : ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(a) form an isosceles triangle
(b) form a right triangle
(c) are collinear
(d) form a scalene triangle
Q6. The p.v.’s of the points A , B , C are i xj 3k , 3i 4 j 7k and yi 2 j 5k respectively are collinear, ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
then x , y ? (a) 2 , 3 Q7. If a
(b) 2 , 3
(c) 2 , 3
(d) 2 , 3
3 and 1 k 2 , then ka lies in the interval:
(a) 0 , 6
(b)
3, 6
(c) 3, 6
(d) 1, 2
Q8. If a and b be two vectors such that a b 2 and a.b 1 , then the angle between a and b is:
(a) 3
(b) 4
(c) 2 3
(d) none of these
Prepared by Amit Bajaj Sir | Downloaded from http://amitbajajmaths.blogspot.com/ http://amitbajajmaths.blogspot.com/
Page 1
The world’s largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
The world’s largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Q9. If a i 2 j 3k and b 3i 2 j 2 k , then angle between a b and a b is: ˆ
ˆ
ˆ
ˆ
(a) 3
ˆ
ˆ
(b) 4
(c) 2
(d) 2 3
(b) a b
(c) a || b
(d) none of these
Q10. If a b a b , then:
(a) a b
Q11. If a , b , c are mutually perpendicular unit vectors, then value of a b c is: ˆ
ˆ
ˆ
ˆ
ˆ
(a) 1
(b)
(c)
2
ˆ
(d) 2
3
Q12. If a b c 0 , a 3, 3 , b 5 , c 7 , then the angle between a and b is:
(b) 2 3
(a) 6
(c) 5 3
(d) 3
be the angle between them, then a b is a unit vector, if: Q13. Let a and b are two unit vectors and be (b) 3
(a) 4
(c) 2 3
(d) 2
and 5i 2 j 4k then cosine of the angle between PQ and y-axis is: Q14. If p.v. of P and Q are i 3 j 7k an ˆ
(a)
5 162
ˆ
ˆ
(b)
4 162
ˆ
ˆ
ˆ
(c)
11 162
(d)
5 162
Q15. If a and b are two unit vectors, then which of the following values of a. b is not possible?
(a)
3
(b)
3 2
(c) 1
2
(d) 1 2
Q16. If a and b are two unit vectors inclined at an angle , then the value of a b is:
(a) 2 sin 2
(b) 2sin
(c) 2 cos 2
(d) 2cos
The world’s largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Q18. If a 2i 3 j k , b i 2 j 4k and c i j k , then a b . a c is: ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(b) 74
(a) 74
ˆ
(d) 52
(c) 52
Q19. The vector b 3i 4k is to be written as the sum of a vector parallel parallel to a i j and a vector ˆ
ˆ
ˆ
ˆ
perpendicular to a . Then is:
(a)
3
i j 2 ˆ
(b)
ˆ
2
i j 3 ˆ
(c)
ˆ
1
i j 2 ˆ
ˆ
(d)
1
i j 3 ˆ
ˆ
Q20. If a i j k , b i 2 j 2k and c i 2 j k , then unit vector normal to vectors a b and b c ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
is: (a) i
(b) j
Q21. If a b 4 , a . b 2 , then a
(a) 6
(c) k
(d) none of these
(c) 20
(d) 8
ˆ
ˆ
ˆ
2
b
2
is:
(b) 2
Q22. If is the angle between any two vectors a and b , then a b a . b when is:
(b) 4
(a) 0
(c) 2
(d)
Q23. The diagonals of a parallelogram are represented by the vectors d1 3i
ˆ
j 2k and d2 i 3 j 4k . ˆ
ˆ
ˆ
ˆ
The area of the parallelogram: (a) 7 3 sq.un sq.unit itss Q24. The value of a b
(a) 0
(b) 5 3 sq.un sq.unit itss
(c) 3 5 sq.un sq.unit itss
(d) none of these
c a , where a 1, b 5 , c 3 , is:
b c (b) 1
(c) 6
(d) none of these
Q25. If a 2i 3 j 5 k , b 3i 4 j 5k and c 5i 3 j 2k , then the volume of the parallelopiped with ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
The world’s largest digital library
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
ANSWERS 1. c
2. b
3. b
4. a
5. a
6. a
7. a
8. c
9. c
10. b
11. c
12. d
15. a
16. a
17. d
18. b
19. a
20. a
21. c
22. b
23. b
24. a
25. d
26. c
13. c
14. d
