# Vector Algebra MCQs Part I

1) If a=4i+6j and b=3j+4k, then the vector form of component of a along
b is

a)
b)
c)
d) 3j+4k

2) The vector
is to be written as the sum of a vector parallel
to
and a vector

a)
b)
c)
d)

3) If

a) u is a unit vector
b) u=a+i+j+k
c) u=2a
d) u=8(i+j+k)

4) The volume of a parallelopiped whose sides are given by
is

a) 4/13
b) 4
c) 2/7
d) none of these

5) If then
the value of

a) 60
b) 64
c) 70
d) -74

6) The scalar
equals

a) 0
b) [ABC]+[BCA]
c) [ABC]
d) none of these

7) Let a=2i-j+k ; b=i+2j-k and c=i+j+2k be three vectors. A vector in the plane
of
b and c whose projection on a is of magnitude
is

a) 2i-3j-3k
b) 2i+3j+3k
c) -2i-j+5k
d) 2i+j+5k

8) If the vectors c, a=xi+yj+zk and b=j are such that a, c, b form a right
handed systems then c is

a) zi-xk
b) 0
c) yj
d) -zi+xk

9) ABCD is a quadrilateral with
If its area is times the area
of adjacent sides, then is equal
to

a) 5
b)
c) 1
d)

10) ABCDEF is a regular hexagon where center O is the origin. If the position
vectors of A and B are respectively
the is equal to

a)
b)
c)
d) none of these

11) The position vectors of two vertices and the centroid of a triangle are
. The position vector of the
third vertex of the triangle is

a)
b)
c)
d) none of these

12) Let the position vectors of the point A,B,C be
respectively. Then the ABC is

a) right angled
b) equilateral
c) isosceles
d) none of these

13) . are three vectors of which
every pair is noncollinear. If the vector
are collinear with

a) a unit vector
b) the null vector
c)
d) none of these

14)
a)
b)
c)
d)

15) The position vectors of three points are
and are noncoplanar vectors. The
points are collinear when

a)
b)
c)
d) None of these

16) are linearly dependent
vectors and then

a)
b)
c)
d)

17) Let A vectors along one of the
bisectors of the angle <AOB is

a)
b)
c)
d) none of these

18) A vector has components 2p and 1 with respect to a rectangular Cartesian
system. The axes are rotated through an angle
about the origin in the anticlockwise sense. If the vector has components
p+1 and 1 with respect to the new system then

a)
b) p=0
c)
d) p=1,-1

19) If are two vectors of magnitude
2 inclined at an angle then
the angle between is

a)
b)
c)
d) None of these

20) Let Then the angle between

a)
b)
c)
d)

21) A vector of magnitude 4 which is equally inclined to the vectors
a)
b)
c)
d) none of these

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

23) Let is
a)
b) 6
c)
d) none of these

24)
a)
b)
c)
d) none of these

25) If
are unit vectors such that
is also a unit vector then the angle between the vectors

a)
b)
c)
d)

26)
a)
b)
c)
d)

27) is
equal to

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

28) is
equal to

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

29) If a,b,c are the pth, qth, rth terms of an HP andthen
a)
b)
c)
d)

30) If
a)
b)
c)
d)

31) Let
a)
b)
c)
d)

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

33) If are
three vectors of equal magnitude and the angle between each pair of vectors
is
such that
is equal to

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

34) If
a) 1
b)
c) 3
d) none of these

35) If
equal to

a)
b)
c)
d) none of these

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

37) Two vectors
a) perpendicular to each other
b) parallel to each other
c)
d)

38) ABC is an equilateral triangle of side a. the value of
a)
b)
c)
d) none of these

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

40)
a) 0
b)
c)
d) 1

41) If
are two noncollinear and nonzero vectors such that where,
a,b,c are the lengths of the sides of a triangle, then the triangle is

a) right angled
b) obtuse angled
c) equilateral
d) isosceles

42) If
are any three vectors such that is

a)
b)
c)
d) none of these

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

44) The vectors are
the sides of a triangle which is

a) equilateral
b) isosceles
c) right angled
d) both b and c

45)
a)
b)
c)
d)

46)
a) an equilateral triangle
b) a right angled triangle
c) an isosceles triangle
d) collinear vectors

47)
a) -3/2
b) 0
c) -1
d) 1

48) Let
a)
b)
c)
d)

49) What is the value of
a) 0
b)
c)
d)

50) The position vectors of the points A and B are
respectively. P divides AB in the ratio 3 : 1. Q is the mid-point of AP. The
position vector of Q is

a)
b)
c)
d)

51)
a) -1
b) 0
c) 2
d) -3

52)
a)
b)
c)
d) none of these

53)
a)
b)
c)
d) none of these

54)
a) 0
b) 1
c)
d)

55) A vector
has components 2p and 1 with respect to a rectangular Cartesian system. This
system is rotated through a certain angle about the origin in the counterclockwise
sense. If, with respect to the new system,
has components p+1 and 1, then

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

56)
a) 0
b) 1
c) 2
d) -2

57) The angle between vectors
a)
b)
c)
d) 0

58)

are
vectors reciprocal to the non-coplanar vectors
then

a)
b) 1
c) 4
d) 0

59) Let be
three non-coplanar vectors and
are vectors defined by the relations
Then the value of the expression

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

60) The value of
a)
b)
c)
d) 0

61) Which one of the following is not a vector?
a) Momentum
b) Velocity
c) Mass
d) Angular velocity

62) What is needed to represent a scalar?
a) a real number only
b) a real number and a unit of measurement
c) a unit of measurement only
d) none of these

63) The magnitude of a vector is
a) unique
b) not unique
c) a unique positive integer
d) not unique but can have only finite number of values

64) If is a unit vector ^
r to , then the second unit vector
^ r  to
is

a)
b)
c)
d)

65) The projection of on OX, OY,
OZ are respectively 12, 3 and 4, then the magnitude of
is

a) 13
b) 169
c) 19
d) 16

66) The angle between the straight lines

a) 0
b)
c)
d)

67) The volume ( in cubic units) of the parallelopiped whose edges are represented
by the vectors

a) 2
b) 0
c)
d)

68) A unit vector normal to the plane through the points
a)
b)
c)
d) none

69) The work done by the force
in moving a particle along a straight line from the point
(3,2,-1) to (2, -1,4) is

a) 0
b) 4
c) 15
d) 19

70) Two like parallel forces P and 3P act on a rigid body at points A and B
respectively. If the forces are interchanged in position, the resultant will
be displaced through a distance of

a)
b)
c)
d)

71) Let
If the point of P on the line segment BC is equidistant from AB and AC then
is

a)
b)
c)
d) none of these

72) Two vectors are said to be equal if
a) their magnitudes are same
b) direction same
c) originate from the same point
d) they have same magnitude and same sense of direction

73) Two vectors a and b are parallel and have equal magnitudes, then
a) they are equal
b) they are not equal
c) they may or not be equal
d) they do not have the same direction

74) If a is non-zero vector of modulus a and m is a non-zero scalar,
then m a is a unit vector if

a)
b)
c)
d) none

75) a and b are two unit vectors and
is the angle between them. Then a+b is a unit vector if

a)
b)
c)
d)

76) The position vectors of A and B are a and b respectively,
then the position vector of a point P which divides AB in the ratio
1:2 is

a)
b)
c)
d)

77) Point A is a+2b, P is a and P divides AB in the ratio 2:3. The position
vector of B is

a) 2a-b
b) b-2a
c) a-3b
d) b

78)
is the angle between the two vectors a and b then

a)
b)
c)
d)

79) If a be a non-zero vector then which of the following is correct?
a) a . a = 0
b) a . a > 0
c)
d)

80) a and b are two non-zero vectors, then (a+b).(a-b) is equal to
a) a + b
b)
c)
d)

81) a.b=0 implies only
a) a=0
b) b=0
c)
d)

82) If a,b,c be three non-zero vectors then the equation a.b=a.c implies
a) b=c
b) a is orthogonal to both b and c
c) a is orthogonal to b-c
d) either b=c or a is orthogonal to b-c

83) If a and b include an angle of
and their magnitudes are 2 and ,
then a.b is equal to

a) 3
b)
c)
d) -3

84) If (i, j, k) be a set of orthogonal unit vectors, then
a) i.i+j.j+k.k=0
b) i.j+j.k+k.i=3
c) i.i=j.j=k.k=1
d) i.j=j.k=k.i=1

85) If
be the angle between the vectors 4(i-k) and i+j+k, then
is

a)
b)
c)
d)

86) The angle between the vectors 2i+ 3j+ k and 2i-j-k is
a)
b)
c)
d) 0

87) If a and b are two vectors, then
is a unit vector if

a)
b)
c)
d) none

88) [a b c] is the scalar triple product of three vectors, a, b and c, then
[a b c] is equal to

a) [b a c]
b) [c b a]
c) [b c a]
d) [a c b]

89) If
is the angle between vectors a and b, then
is equal to

a) 0
b)
c)
d)

90)
is equal to

a) (a.b)c-(b.c)b
b) (a.b)a+(a.b)c
c) (b.c)a-(b.c)b
d) (a.c)b-(a.b)c

91) ,
then

a) u is a unit vector
b) u=a+b+c
c) u=0
d)

92) If a= 4i+2j-5k, b=-12i-6j+15k, then the vectors a, b are
a) orthogonal
b) parallel
c) non-coplanar
d) none of these

93) If [i, j, k] be orthogonal set of unit vectors, then
a)
b)
c)
d)

94) If the position vectors of three points are, a-2b+3c, 2a+3b-4c, -7b+10c,
then the three points are

a) collinear
b) coplanar
c) non-collinear
d) neither

95) If a+b+c=0, then
the angle between a and b is

a)
b)
c)
d)

96) If a, b, c are any three coplanar unit vectors, then
a)
b)
c)
d)

97) If a.b=a.c and
then

a) a is perpendicular to b-c
b) a is parellel to b-c
c) either a=0 or b=c
d) none of these

98) If
then (a+b).(a-b) is

a) +ive
b) -ive
c) zero
d) none of these

99) The vector 2i+j-k is perpendicular to i-4j+,
if
is equal to

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

100) The area of parallelogram having diagonals a=3i+j-2k and b=i-3j+4k is
a)
b)
c) 8
d) 4