Scalars and Vectors
8. If Fx = 11 N and Fy = 11 N then the angle between Fx
and Fy is:
(a) 30o
(b) 45o
(c) 60o
(d) 90o
9. If A B o and A x B = o then
(a) Either A or B or both are null vectors.
(b) A and B are parallel to each other
(c) A and B are perpendicular to each other
(d) A and B are opposite to each other
10. The product of mass and velocity of a body is called:
(a) Torque
(b) Force
(c) Kinetic energy
(d) Momentum
11. Angle “O” which a vector makes with +x-axis in
anticlockwise direction. When its x-component is
positive and y-component is negative, will be:
(a) 90o< O < 180o
(b) 180o< O < 270o
(c) 270o< O < 360o
(d) 0o < O < 90o
12. When dot product of two vectors A and B is zero,
then :
(a) Either A or B or both are null vectors.
(b) A  is perpendicular to B
(c) A is parallel ; B
(d) A and b
(e) A and c
13. Magnitude of dot product of two vectors is
maximum when:
(a) Vectors are of maximum value
(b) Vectors are perpendicular to each other
(c) Vectors are parallel to each other
(d) None of these.
1. When a vector is multiplied by a negative number its
direction changes by an angle of:
(a) 00 (b) 900 (c) 1800 (d) 3600
2. A vector of magnitude “1” is called:
(a) Resultant vector (b) null vector (c)
(d) Small vector
unit vector
3. Unit vectors are used to specify:
(a) Magnitude of a vector
(b) Direction of a vector
(c) Magnitude as well as direction of a vector
(d) Unit of other vectors
(e)
4. If Ax. Au and Az represent magnitudes of components
of a vector A>, then the magnitude of vector A > is given
by:
(a) A - Ax + Au + Az
(b) A - Ax2 + Au2 + Az2
(c)
(d) 2 =
5. Law of Cosine used to find:
(a) Magnitude of dot product of two vectors
(b) Direction of dot product of two vectors
(c) Magnitude of resultant of two vectors
(d) Direction of resultant of two vectors.
6. Law of Sites can be used to find the:
(a) Direction of resultant of two vectors.
(b) Magnitude of resultant of two vectors.
(c) Magnitude of cross product of two vectors.
(d) Direction of cross product of two vectors.
7. ………………………is a vector quantity.
(a) Mass
(b) Distance
(c) Torque
(d) Work
14. According to commutative law:
(a) A . B =AB
(b) A . B = BA
(c) A . B = B . A
(d) B . A = BA
15. Dot product of two vectors gives;
(a) A scalar quantity
(b) A vector quantity
(c) A number
(d) Sometimes a scalar sometimes a vector
quantity.
(19)
(a)
(b)
(c)
(d)
A-> x B-> = B-> x A-> because:
Their magnitude is equal but direction is different
Their direction and magnitude both are different
Their direction is same but magnitude is different
None of the above
(20) Unit vector perpendicular to the plane of A-> and
B-> is given by:
(a) U =
(b)U =
16. | .
|= 0 because
(b) U =
(a) and
are unit vectors
(b)
and
are null vectors
(c)
and
are perpendicular to each other
(e) U=
(d) and are parallel to each other
17.
.
21 .Cross product f two vectors give:
(a) A scalar quantity
(b) A vector quantity
(c) A number
(d) Sometimes a scalar sometimes a vector quantity.
22. Cross product of two vectors has a maximum value
when:
(a) The magnitude of vectors is maximum
(b) When vectors are parallel to each other.
(c) When vectors are perpendicular to each other.
= 1 because:
(a) is a unit vector
23. Cross product of two vectors
and
is zero, then.
(b) is parallel to
(a) Either or both
(c)
(b)
is perpendicular to
and
are null vectors.
is perpendicular to
(c) A is parallel to
(d) a and b
(e) a and c
(d) A and B
(e) A and c
18. A unit vector parallel to vector
is given by:
24.
X
(a)
=
by:
(b)
=
(a) A B Cos
(b) A B Sin
(c) A B Tan
(c)
=
,
(d) none of these
(d)
B is a vector quantity its magnitude is given
25.
x
is a vector quantity its direction can be
determined by:
(a)
(b)
(c)
(d)
Head o tail rule
Left hand rule
Right hand rule
Law of Sines
30. Magnitude of
(a) 1
(b) -1
(c) 0
(d)
31.
26.
.
by?
(d)
32. ………………is an example of dot
(a)
(b)
(c)
(d)
27. Dot product of vectors obeys:
(a)
(b)
(c)
(d)
(e)
Commutative law
Distributive law.
Law of Sines.
A and B
A and C.
is equal to.
(a) 1
(b) -1
(c) 0
(d)
Is a scalar quantity its magnitude is given
(a) A B Cos
(b) A B Sin
(c) A B Tan
X
x
Acceleration
Momentum
Torque
Power.
33. The resultant of 3 N and 4 N acting perpendicularly
on? Body is
(a)
(b)
(c)
(d)
28. X = 0 because
1N
2N
5N
7N
34. Angle between vector
a)
Is a unit vector.
b) is parallel to
c)
is perpendicular to
d) A and b.
e) A and c
29.
a)
b)
c)
d)
X j x = k because:
and both are unit vector
and both are unit vectors perpendicular to
x gives a unit vector perpendicular to
X
gives a unit vector perpendicular to the
plane of
and .
product of vectors.
(a)
(b)
(c)
(d)
and
is:
0o
45o
90o
180o
35. The dot product of two unit vectors perpendicular to one
another is:
a)
b)
c)
d)
0 (zero)
1
-1
+1
36. The value of k. (
(a) 0
(b) 1
(c)
x
) is:
37. If the vector addition of two vectors of magnitude
3 units and 4 units has a resultant of 5 units, then the
angle between those two vectors is:
(a)
(b)
(c)
(d)
0
45o
90o
180o
44.
A unit vector
Null vector
Same vector
Position vector
30
-30
7
3.33
Vectors are in the same direction.
Vectors are perpendicular.
Vectors are opposite.
Vectors are very small
41. If
and
a)
.
b)
.
c)
x
are tow vectors then:
=
.
=
=
.
x
42. If the vector addition of two vectors of magnitude 3
units and 4 units has a resultant of 5 units, then
the
angle between those two vectors is:
(1-b ii, 1996)
a) 0o
b) 45o
c) 90o
a)
b)
c)
d)
is equal to (3-a I pre med 03)
J2
J
One
Zero
a)
b)
c)
d)
Unit vector
Position vector
Null vector
Free vector
46. The dot product of unit vector
med 03)
40. If cross product of two none zeros vectors is zero
then:
(a)
(b)
(c)
(d)
X
45. If a vector quantity is divided by its magnitude the
vector obtained is called (1-a iii pre med 03)
39. A force of magnitude 10 N acting on a body
produces a displacement of 3 m such that the force
and displacement are in opposite direction. Their dot
product will be:
(a)
(b)
(c)
(d)
) has value: (1 – a ii, 2001, 1- a iii, pre-
a) Zero
b) One
c)
d)
o
38. The resultant of two equal and opposite vectors
is:
(a)
(b)
(c)
(d)
43.
( X
eng.2002)
&
is: (2-a iii pre
a) Zero
b) 1
c) -1
d)
47. If
= 4i – 2j and
= 3j, the work done will be
(2-a ii pre eng 03)
a)
b)
c)
d)
48. If
4 joule
8 joule
2 joule
12 joule
.
= o when
vectors are
a) Parallel
b) Opposite
c) Perpendicular
= o,
1a – ii, 04)
= o the two
49. When |
+
vectors
|=|
and
–
|, the angle between the
is: (1a-iii, 04)
a) Zero
b) 45o
c) 90o
50. If
.
= O and
vector B is:
x
= O and
O the
(1a-ii, 05)
55. Two perpendicular vectors having magnitudes of 4
units and 3 units are added, their resultant has the
magnitude of:
(2-xvi, 2009)
a) 7 units
b) 12 units
c) 25 units
d) 5 units
56. If
a) Equal to
.
= O and
x
= O, then vector
is:
a) Equal to
b) Zero
c) Perpendicular to
d) Parallel to
b) Zero
c) Perpendicular to
d) Parallel to
(***** 2010)
51. The area of a parallelogram formed by two vectors
and
is given by: (1a-ii, 07)
a) ½
b) |
.
X
d)
X
.
vector
is:
= O and
1-vii, 2011)
a) Equal to
|
)
52. Two perpendicular vectors having magnitudes of 4
units and 3 units are added. Their resultant has a
magnitude of:
(1a-ii, 08)
a) 7 units
b) 12 units
c) 25 units
d) 5 units
53. If , and are the unit vectors along x-y and z-axes
respectively, then k x j = (2-viii,
(a)
(b)
(c) 1
(d) -1
54. If a vector is divided by its own magnitude, the
resulting vector is called: 2-xi, 2009)
a)
b)
c)
d)
.
)
|
c) ½ |
57. If
Position vector
Unit vector
Null vector
Free vector
b) Zero
c) Perpendicular to
d) Parallel to
x
= O and
x O then
ANSWERS
1. 180o
2. Unit vector
3. Direction of a vector
4.
5.
6.
7.
8.
9.
.
=
42. 90o
2
2
2
A=
x + Ay + Az
Magnitude of the resultant of two vectors
Direction of resultant of two vectors
Torque
45o
Either or both are null vectors.
10. Momentum
11. 270o < 0 < 360o
12. A and b
13. Vectors are parallel to each other
14. .
=
.
15. A scalar quantity.
16. And are perpendicular to each other.
17. A and b
18. =
/| |
43. One
44. Zero
45. Unit vector
46. Zero
47. 4 Joules
48. Perpendicular
49. 90o
50. Zero
51. |
X
|
52. 5 units
19. Their magnitude is equal but their direction is different
20.
= . X
/| . x
|
21. A vector quantity.
22. When vectors are perpendicular.
23. A and c
24. A B Sin 0
25. Right hand rule
26. A B Cos 0
27. A and b
28. is perpendicular to
29. x gives a unit vector perpendicular to the plane of and
30. -1
31. –
32. Power
33. 5 N
34. 90o
35. 0
36. 1
37. 90o
38. Null vector
39. – 30 J
40. Vectors are in the same direction
53. –
54. Units vector
55. Units
56. Zero
57. Zero.
.