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
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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
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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
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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