# Vector Algebra MCQs Part III

1)
a)
b)
c)
d) none of these

2)
a)
b)
c)
d)

3)
a)
b)
c)
d)

4)
a)
b)
c)
d) none of these

5) If
a) 7
b) 5
c) 13
d)

6)
a)
b)
c)
d) none of these

7)
a)
b)
c)
d)

8)
a) – 4
b) -1
c) 4
d) – 2

9)
a) -1

b) 0
c) 1
d) Both (a) and (c)

10)
a) 2
b) 3
c) 0
d) none of these

11) For any three vectors
a)
b)
c)
d) none of these

12)
a)
b)
c)
d)

13) For any three vectors
a)
b)
c)
d)

14)
a) 0
b) 1
c) 2
d) -1

15)
a) 0
b)
c)
d)

16)
a) -1
b) 0
c) 1
d) none of these

17)
a) 0
b) 1
c) 2
d) 3

18)
a) 0
b) 1
c)
d)

19)
a)
b)
c)
d)

20)
a) p=0
b)
c)
d) p=1 or p= -1

21) If are
non-coplanar vectors, then

a)
b)
c)
d) none of these

22)
equals

a)
b)
c)
d) none of these

23)
a)
b)
c)
d) none of these.

24)
a)
b)
c)
d)

25) If
the constant forces

act on a particle due to which it is displaced from a point
then
the work done by the forces is

a) 15 units
b) -15 units
c) 9 units
d) -9 units

26) The work done by the force
in moving an object along the vector

a) -9 units
b) 15 units
c) 9 units
d) none of these

27) If forces of magnitudes 6 and
7 units acting in the directions

respectively act on a particle which is displaced from the point
,
then the work done by the forces is

a) 4 units
b) -4 units
c) 7 units
d) -7 units

28) If
the force represented by

is acting through the point

then its moment about the point

is

a)
b)
c)
d)

29) The
moment of the couple formed by the forces

respectively is

a)
b)
c)
d)

30) A force of 39 kg.wt is acting
at a point

The moment of this force about a line through the origin having the direction
of

is

a) 76 units
b) -76 units
c)
d) none of these

31) A,
B have position vectors

relative to the origin O and X, Y divide

internally and externally respectively in the ratio 2 : 1.

a)
b)
c)
d)

32)
a)
b)
c)
d) none of these

33) The
projection of the vector

on the axis making equal acute
angles with the coordinate axes is

a) 3
b)
c)
d) none of these.

34) If
is vector of magnitude 50 collinear with the vector

and makes an acute angle with
the positive direction of z-axis, then

a)
b)
c)
d) none of these

35)
a) 11
b) -11
c) 33
d) -33

36) The
unit vectors orthogonal to the vector
and
making equal angles with the X and Y axis is (are)

a)
b)
c)
d) none of these

37) Consider
a tetrahedron with faces

be the vectors whose magnitudes are respectively equal to areas of

and whose directions are perpendicular to these faces in outward direction. Then
equals

a) 1
b) 4
c) 0
d) none of these

38) A
vector which makes equal angles with the vectors

a)
b)
c)
d) Both (b) and ( c).

39) Let
a,b,c be distinct non-negative numbers. If the vectors

lie in a plane, then c is the

a) AM of a and b
b) GM of a and b
c) HM of a and b
d) none of these

40) If
a vector

is directed along the bisector of the angle between the vectors

a)
b)
c)
d) Both (a) and (c)

41) If
the vectors
are
inclined at an acute angle, then

a) a = 0
b) a < 0
c) a > 0
d) none of these

42) If

are three non-zero vectors such that
,
then

a) m < 0
b) m > 0
c) m = 0
d) m = 3.

43) Let
be three vectors. A vector in the plane of

whose projection on

a)
b)
c)
d) Both (a) and (c)

44) Let
are three non-coplanar vectors such that

a)
b)
c)
d) Both (b) and ( c).

45) If

are three non-coplanar vectors such that

a)
b)
c)
d)

46)
a)
b)
c)
d)

47) Let
be three non-zero vectors such
that no two of which are
collinear
and the vector

a)
b)
c)
d) none of these

48) A
parallelogram is constructed on the vectors

then the length of a diagonal of the parallelogram is

a)
b)
c)
d) none of these

49)
a) 47
b) -25
c) 0
d) 25

50) If are
three non-coplanar vectors, then

equals

a) 0
b)
c)
d)

51) If
are non-coplanar unit vectors such that

a)
b)
c)
d)

52) Let

be distinct real numbers. The points with position vectors

a) are collinear
b) form an equilateral triangle
c) form a scalene triangle
d) form a right angled triangle

53) Let

be the position vectors of P and Q respectively, with respect to O and

The points R and S divide PQ internally and externally in the ration 2:3 respectively.
If
are
perpendicular, then

a)
b)
c)
d)

54) The vector
is

a) unit vector
b)
c)
d) All the above.

55)
a)
b)
c)
d)

56) The
number of vectors of unit length

to the vectors

a) one
b) two
c) three
d) infinite

57)
a) 0
b)
c)
d) none of these

58) The vector
lies in the plane of vectors

which of the following is correct

a)
b)
c)
d)

59) A unit vector perpendicular
to

a)
b)
c)
d) none of these

60) A tetrahedron has vertices at O (0,
0, 0), A (1, 2, 1), B (2, 1, 3) and C (-1, 1, 2). Then the angle between the
faces OAB and ABC will be

a)
b)
c)
d) none of these

61)
a)
b)
c)
d) 0

62)

are three non-coplanar vectors, then the value of the expression

a) 3
b) 2
c) 1
d) 0

63)

The points with position vectors

are collinear if

a) a = -40
b) a = 40
c) a = 20
d) none of these

64) The
points with position vectors

are collinear if the value of a is

a) -8
b) 4
c) 8
d) 12

65) If
C is the middle point of AB and P is any point outside AB, then

a)
b)
c)
d)

66) The
value of b such that the scalar product of the vector

with the unit vector parallel
to the sum of the vectors

a) -2
b) -1
c) 0
d) 1

67)
a) 12
b) 2
c) 0
d) -12

68)
a) 16
b) 8
c) 3
d) 12

69) The value of c so that for all
real x, the vectors

make an obtuse angle are

a) c < 0
b)
c)
d) c > 0

70)
a) 6
b) 5
c) 4
d) 3

71) The median AD of the triangle
ABC is bisected at E, BE meets AC in F, then AF: AC =

a)
b)
c)
d)

72) If the vectors
and

are coplanar, then x =

a)
b)
c) 0
d) 1

73) Volume of the parallelopiped
whose coterminal edges are

is

a) 5 units
b) 6 units
c) 7 units
d) 8 units

74)
is not perpendicular to

a)
b)
c)
d)

75) If

are unit orthonormal vectors and

is a vector, if

then

is

a) 0
b) 1
c) -1
d) arbitrary scalar

76) The area of the parallelogram whose
diagonals are the vectors

and

where

and
are
the unit vectors forming an angle of

is

a)
b)
c)
d) none of these

77)

is equal to

a)
b)
c)
d) 0

78)

In the trapezoid the vector
We will then find that

a)
b)
c)
d)

79)

The vector
is perpendicular to the vectors
and
satisfying the condition

a)
b)
c)
d) none of these

80)
a)
b)
c)
d)

81)
be any three non-zero non-coplanar vectors, then any vector
,
is equal to

a)
b)
c)
d) none of these

82)

The vector
coplanar with the vectors

perpendicular to the vector

a)
b)
c)
d) none of these

83)
a)
b)
c)
d) none of these

84) A unit vector in xy-plane makes
an angle of

a)
b)
c)
d) none of these

85)
a) 1
b)
c) 0
d) none of these

86)
a)
b)
c)
d) None of these

87) If are unit vectors and is
the angle between them, then

a)
b)
c)
d)

88) If
a)
b)
c)
d) none of these

89) If
a)
b)
c)
d)

90) The vectors and

include an acute angle for

a) all real m
b) m<-2 or m>-1/2
c) m=-1/2
d)

91)

a) 0
b) 1
c) 2
d) 3

92) Three numbers form an increasing G. P. If the middle
number be doubled, then the new numbers are in A.
P. the common ratio of the G. P is

a)
b)
c)
d)

93)
a) 0
b)
c)
d)

94) The length of the longer diagonal of the parallelogram whose adjacent
sides are along

and
angle between

a)
b)
c)
d)

95) The number of vectors of unit length perpendicular to the vectors

a) 1
b) 2
c) 4
d) infinite

96) The value of
a)
b)
c) 0
d) none of these

97) For non-coplanar vectors
a)
b)
c)
d)

98) If
are unit vectors such that the vector
is perpendicular to
is perpendicular to
then the angle between

a)
b)
c)
d)

99)
a)
b)
c)
d)

100) Let then
satisfying

a)
b)
c)
d)