MUMBAI / DELHI / AKOLA / LUCKNOW / KOLKATA / NASHIK

Time : TW TEST ( VECTORS ) Max. Marks :

1. Forces 3N , 4N and 12N act at a point in mutually perpendicular directions. The magnitude of resultant force in
Newton is
(a) 12 (b) 13 (c) 7 (d) 19

2. The scalar product of two vectors is 6 3 and the magnitude of their vector product is 6, then the angle between
the two vectors is
(a) 90
0
(b) 60
0
(c) 45
0
(d) 30
0



3. If k

6 j

2 i

4 A + =

& k

3 j

2 i

B =

, the angle, which B A

+ makes with x-axis, is
(a) cos
-1
(
50
3
) (b) cos
-1
(
50
5
) (c) cos
-1
(
50
4
) (d) cos
-1
(
50
12
)

4. Given j

8 i

6 B

& j

4 i

3 A + = + =

which of the following statement is incorrect

(a) 0 B A =

(b)
2
1
B
A
=

(c) A

=15 (d) B A

=40

5. The resultant of two forces 5 Newton and 10 Newton can never be
(a) 12 N (b) 5 N (c) 10 N (d) 4 N


6. If the magnitude of resultant of two forces F and F acting at a point is also F, then the angle between
the two forces is
(a) 0
o
(b) 60
o
(c) 120
o
(d) 90
o


7. If | x |, a b a b - =


then the value of |a b +

| is
(a)
2 2
a b + (b) a +b
(c)
2 2
2ab a b + + (d)
2 2
2
ab
a b

+ +
`
)


8.


0.4 0.8 i j ck + + represents a unit vector when c is
(a) -0.2 (b) 0.20 (c) 0.80 (d) 0

9. The vectors

( ) i j k + + and 3

i form two sides of a triangle. The area of the triangle is

(a) 3 (b)2 3 (c)
3
2
(d) 3 2
10. Two forces of magnitudes P and 3P act at right angles to each other. Their resultant makes an angle
u with P; which of the following gives the correct value of u?
(a) 30
o
(b) 45
o
(c) 60
o
(d) none of the above

11. Three sets of forces act on a particle whose resultant can non be zero
(a) 10. 10. 10 (b)10,10,20 (c)10,20,20 (d) 10, 20, 40

12. ABCDEF is a regular hexagon. What is the value of AB AC AD AE AF + + + +

?

(a)0

(b)2AO

(c)4AO

(d) 6AO

13. Two vectors and A B

are inclined at an angle 45
0
have resultant R

which makes an angle 30

o
with A

.
If the direction of and A B

are interchanged, then the resultant will have the same.
(a)magnitude (b)direction
(c)bothmagnitude and direction (d) none

14. Given P A BandQ A B. = + = If the magnitudes of P and Q are equal, the angle between vectors A
and B is
(a)zero (b) 45
0
(c) 90
0
(d) 180
0

15. If j

4 i

3 a + =

and j

24 i

7 b + =

, the vector having the same magnitude as b

and parallel to a

, is
(a) j

17 i

4 + (b) j

20 i

15 + (c) j

15 i

16 + (d) j

20 i

10 +

16. If A

+B

+C

=O

and |A

| =2; |B

| =4, Which of the following cant be correct?

(a) |C

| =2 (b)|C

| =6 (c) |C

| =8 (d) |C

| =4

17. The direction cosines of A

=i

+2j

+3k

are
(a)
14
1
,
14
2
,
14
3
(b) 1, 2, 3 (c)
4
1
,
4
2
,
4
3
(d) none of these.

18. A person moves 30m north, then 40m east and then 50m south-west. His displacement from the original
position is nearly
(a) 120 m (b) 100 m (c) 70 m (d) zero

19. A particle moves fromA (-2, -4, 0) to B (4, 5, 6), the displacement vector of point is
(a)

9i 6j 6k + + (b)

6i 9j 6k + + (c)

6i 9j + (d)

9i 6j +

20. The resultant of B & A

makes an angle o with A

and | with B

then
(a)o<|always (b)o>| if A <B
(c)o<| if A =B (d)o<| if A <B .
21. If 2 | A | =

and | B |

=4, angle between them is 60
0
, | B A |

is
(a) 13 (b) 3 3 (c) 3 (d) 2 3

22. If three vectors along coordinate axis represent the adjacent sides of a cube of side b, then the unit vector
along its diagonal passing through the origin will be
(a)
2
k

+ +
(b)
b 3
k

+ +
(c) k

+ + (d)
3
k

+ +


23. If C , B , A represent unit vectors in each case, which vector combination(s) result in a unit vector ?
(1)
V C
V B
V A

(2)
V C
VB
V
A

(3)
V
C
VB
V
A

(4)
V C
V B
V A

(a)1, 2,3 (b) 1, 3 (c) 1, 2, 4 (d) 4

24. A particle undergoes three successive displacements given by
1
s

= 2 mNorth-East
2
s

=2m due south and

3
s

=4m, 30
0
north of west, then magnitude of net displacement is
(a) 3 4 14+ (b) 3 4 14 (c) 14 (d) none of these

25. Two vectors A

and B

are given as A

= X i +2j +2k , B

=2i 4j +Xk. If A

and B

are perpendicular
then X is equal to
(a) 2 (b) 3 (c) 1 (d) 4

26.Two vectors A

and B

are given as A

= X i +2j +2k , B

=2i 4j +Y k, If A

and B

are parallel
then
(a) X = -1 , Y = - 4 (b) X = -1 , Y = - 2 (c) X = -2 , Y = - 1 ( d) X = 1 , Y = 4

27. Two vectors A

and B

are such that A B C + =

and
2 2 2
A B C + = .
If u is the angle between positive direction of A

and B

then the correct statement is

(a)u = t (b)
2
3
t
u = (c) 0 u = (d)
2
t
u =

28. Given that P Q R 0 + + =

. Two out of the three vectors are equal in magnitude of the third vector is 2
times that of the other two. Which of the following can be angles between these vectors?
(a)
0 0 0
90 ,135,135 (b)
0 0 0
45,45,90
(c)
0 0 0
30 ,60,90 (d)
0 0 0
45,90,135

29. A force
( )

3i 4j + newton acts on a body and displace it by
( )

3i 4j + meter. The work done by the force
is
(a) 5 J (b) 25 J (c) 10 J (d) 30 J

30. Unit vector parallel to the resultant of vectors

A 4i 3j =

and

B 8i 8j = +

will be
(a)

24i 5j
13
+
(b)

12i 5j
13
+
(c)

6i 5j
13
+
(d) None of these

31. The value of n so that vectors

2i 3j 2k,5i nj k + + + and

i 2j 3k + + may be coplanar, will be
(a) 18 (b) 28 (c) 9 (d) 36

32. Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N
respectively. The smaller force will be equal to
(a) 5N (b) 4 N (c) 2 N (d) 1 N

33. The component of vector

A 2i 3j = +

along the vector

i j + is
(a)
5
2
(b) 10 2 (c)5 2 (d) 5

34. The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also
doubled. The angle between the two forces is
(a)
0
60 (b)
0
120 (c)
0
70 (d)
0
180

35. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the
two forces. The angle between the two forces is
(a)
0
120 (b)
0
60 (c)
0
90 (d)
0
150

36. Three vectors satisfy the relation A B 0 =

and A C 0 =

, then A

is parallel to
(a)C

(b) B

(c)B C

(d)B C



37. If A B 3A B =

, then the value of A B +

is
(a)( )
12
2 2
A B AB + + (b)
12
2 2
AB
A B
3
| |
+ +
|
\ .

(c) (A +B) (d)
( )
12
2 2
A B 3AB + +

38. If the angle between the vectors A

and B

is u, the value of the product

( )
B A A

is equal to
(a)
2
BA cosu (b)
2
BA sinu (c)
2
BA sin cos u u (d) zero

39. The (x, y, z) co ordinates of two points A and B are given respectively as (0, 3, -1) and (-2, 6, 4). The
displacement vector from A to B is given by
(a)

2i 6j 4k + + (b)

2i 3j 3k + + (c)

2i 3j 5k + + (d)

2i 3j 5k

40. The sum of two vectors A

and B

is at right angles to their difference. Then

(a) A =B (b) A =2B
(c) B =2A (d)A

and B

have the same direction

41. If
1 2
a and a

are two non collinear unit vectors and if
1 2
a +a = 3

, then the value of
( ) ( )
1 2 1 2
a - a . 2a +a

is
(a) 1/2 (b) 2/3 (c) 2 (d) 1

42. The resultant of
P

and Q

is
R

. If Q

is doubled,
R

is doubled ; when Q

is reversed,
R

is again
doubled, then P : Q : R is
(a) 2: 3: 2
(b)
3: 2: 3
(c)
1: 2: 3
(d)
3: 2: 3


For questions 43, 44 and 45

Three vectors A

, B

and C

are given as 5k 4j 3i A + + =

, 25k - 24j 7i B + =

, 10k - 8j 6i C + =

43. A bird is flying along the vector A with speed 152 m/s then its velocity vector ( in m/s ) will be
(a) 15k 12j 9i + + (b) 5k - 4j 3i + (c) 15k - 3j 12i + (d) 3k - 12j 15i +

44. A vector which is parallel to vector A and has magnitude equal to that of vector C is given by
(a) 10k 8j 6i + + (b) 10k 8j 6i + (c) 5k - 12j 9i + (d) 10k - 8j 6i +

45. What vector should be added to sum of all three vectors A, B and C such that the resultant will be a
unit vector along positive x-axis ?
(a)
30k 36j - 15i - +
(b)
30k 34j - 12i - +
(c)
24k 16j - 10i - +
(d) Not possible