# Vector Algebra MCQs Part V

1) The vector equation of
the plane containing the line
and the point

a)
b)
c)
d) none of these

2) The
point of intersection of the lines

a)
b)
c)
d)

3) The length of
from the origin of the line

a)
b) 2
c)
d) 6

4) The angle between the
lineand
the normal to the plane
is

a)
b)
c)
d)

5) The vector equation
of the plane containing the lines

a)
b)
c)
d) None of these

6) The distance between
the planes given by and

a) 1 unit
b) 13 unit
c) 13/3 unit
d) none of these

7) The centre of the circle
given by

a) (0,1,2)
b) (1,3,4)
c) (-1,3,4)
d) None of these

8) The equation of a plane
through the intersection of the planes
and
and passing through the point (2,1,-1) is

a)
b)
c)
d) none of these

9) The
position vector of a point at a distance of
units from
on a line passing through the points
is

a)
b)
c)
d)

10) A sphere is described
on the join of the points A and B, having position vectors
and respectively
as diameter. The centre of the sphere is

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

11) The distance between
the line

a)
b)
c)
d) None of these

12) If
is
the position vector of one end of diameter of the sphere
then
the position vector of the other end is

a)
b)
c)
d) None of these

13) The position vector
of the centre of the sphere

a)
b)
c)
d)

14) The radius of the circular
section of the sphere cut
by the plane

a) 3
b) 4
c) 5
d) 9

15) A non-zero vector
is parallel to the line of intersection of the plane determined by the vectors and
the plane determined by the vectors .
The angle between

a)
b)
c)
d) None of these

16) If three lines through
the origin and parallel to the vectors
are coplanar, then the value of

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

17) If
be four points such that
.
Then the lines PQ and RS are

a) skew
b) intersect
c) parallel
d) none of these

18) Let
be a unit vector perpendicular to unit vectors if
the angle between

a)
b)
c)
d) none of these

19)
a)
b)
c)
d) none of these

20) The area of the parallelogram whose diagonals represent the vectors
a)
b)
c) 8
d) 4

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

22) A unit vector perpendicular to the plane passing through the point whose
position vectors are

a)
b)
c)
d) none of these

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

24) For three noncoplanar vectors
the relations
holds if and only if

a)
b)
c)
d)

25)
a)
b)
c)
d) 0

26)
a)
b)
c) 0
d) none of these

27) Let
be three unit vectors an

is equal to

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

28) Let
be three distinct positive real numbers. If
then
b is

a) the AM of a,c
b) the GM of a,c
c) the HM of a,c
d) equal to 0

29) If
is equal to

a) 3
b) 1
c) -1
d) none of these

30)

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

31) If
are three noncoplanar vectors represented by concurrent edges of
a parallelepiped of volume 4 then
is equal to

a) 12
b) 4
c)
d) 0

32) If
are three noncoplanar nonzero vectors then
is equal to

a)
b)
c)
d) none of these

33) Let

a) 2
b) 1
c) 0
d) none of these

34) If
are any three vectors in space then
is equal to

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

35) If
are three noncoplanar vectors then
is equal to

a) 0
b)
c)
d)

36)
is equal to

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

37) If
are nonzero and noncollinear vectors then
is equal to

a)
b)
c)
d)

38) The three concurrent edges of a parallelepiped represent the vectors
Then the volume of the paralleepiped whose three concurrent edges are
the three concurrent diagonals of three faces of the given parallelepiped
is

a)
b)
c)
d) none of these

39)
is equal to

a)
b)
c)
d) none of these

40) Let be
three vectors having magnitudes 1, 1 and 2 respectively. If

a)
b)
c)
d) none of these

41) If
is equal to

a)
b)
c)
d) none of these

42)
a)
b)
c)
d) none of these

43) Let
be three mutually perpendicular vectors of the same magnitude. If a vector
satisfied
the equation
then
is given by

a)
b)
c)
d)

44) If . and x represent dot product and cross product respectively then which
of the following is meaningless?

a)
b)
c)
d)

45)
is equal to

a)
b)
c)
d) none of these

46) If
is equal to

a)
b)
c)
d) none of these

47) If
are noncoplanar nonzero vectors then
is equal to

a)
b)
c)
d) none of these

48) If
are three noncoplanar nonzero vectors and
is any vector in space then
is
equal to

a)
b)
c)
d) none of these

49) Let
be three unit vectors of which
are nonparallel. Let the angle between
then

a)
b)
c)
d) none of these

50) Let
and the angle between
is equal to

a)
b)
c) 2
d) 3

51) Let
a)
b)
c)
d)

52) If
be three vectors such that is
equal to

a) 8
b) 16
c) 64
d) none of these

53) If
then
is equal to

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

54)
a) linearly dependent
b) equal vectors
c) parallel vectors
d) none of these

55) is equal
to

a)
b)
c)
d) none of these

56) If the vectors
and is equal to

a)
b)
c)
d) none of these

57) If is equal
to

a) 0
b) 1
c) 2
d) none of these

58) Let
where O,A and C are noncollinear points. Let p denotes the area of the quadrilateral
OABC, and q denotes the area of the parallelogram with OA and OC as adjacent
sides. The p/q is equal to

a) 4
b) 6
c)
d) none of these

59) The position vectors of the vertices A,B,C of a triangle
are respectively.
The length of the bisector AD of the angle BAC where D is on the line segment
BC, is

a)
b)
c)
d) none of these

60) The cosine of the angle between two diagonals of a cube
is

a)
b)
c)
d) none of these

61)
then the length of the perpendicular from A to the line BC is

a)
b)
c)
d) none of these

62) The projection of the vector
on the line whose vector equation is being
the scalalr parameter, is

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

63) A line passes through the points whose position vectors
are The
positions vector of a point on it at a unit distance from the first point is

a)
b)
c)
d) both a and b

64) A vector of magniture 2 along a bisector of the angle between
the two vectors
is

a)
b)
c)
d) both a and c

65) A unit vector coplanar with
a)
b)
c) both a and d
d)

66) A unit vector which is equally inclined to the vectors,
and

a)
b)
c) both a and d
d)

67) If
is equal to

a) 48
b) 16
c)
d) both b and c

68) Three points whose position vectors are
will be collinear if

a)
b)
c)
d) both a and b

69) Let
and it lies in the x-y plane. A vector in the x-y plane having projections 1
and 2 along
is

a)
b)
c)
d) both (a) and (c)

70) If
are noncoplanar nonzero vectors and
is any vector in space then
is equal to

a)
b)
c)
d) both b and c

71) If
are noncoplanar vectors such that
then

a)
b)
c)
d) All the above

72) Let
be noncoplanar vectors and

a)
b)
c)
d) both a and b

73) If
are any three vectors then
is a vector

a)
b)
c)
d) both a and b

74) If
a)
b)
c)
d) both (b) and (c)

75) If
a)
b)
c)
d) both b and c

76)
is equal to

a)
b)
c)
d) all of these

77) If
is a vector

a)
b)
c)
d) both (b) and (c)

78) P is a point on the line through the point A whose position
vector is
and the line is parallel to the vector .
If PA=6, the position vector of P is

a)
b)
c)
d)

79) If P is a point in space such that OP = 12 and
is inclined at angles of
and
with OX and OY respectively, then the position vector of P is

a)
b)
c)
d) None of these

80) The unit vector perpendicular to both the vectors
and making an acute angle with the vector
is

a)
b)
c)
d) none of these

81) The value of
such that (x,y,z)(0,0,0)and

a) 0,2
b) -1,2
c) 0,-1
d) none of these

82) If the unit vectors
are inclined at an angle
such that lies
in the interval

a)
b)
c)
d) both a and b

83) The value of b such that the scalar product of the vector
with the unit vector parallel to the sum of the vector
and
is one is

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

84) Vector
has components 2p and 1 with respect to a rectangular cartesian system. The
system is rotated through a certain angle about the origin in the counter clockwise
sense. If with respect to new system ,
has components p+1 and 1, then

a) p=0
b) p=1 or p=-1/3
c) p=-1 or p=1/3
d) p=1 or p=-1

85) If the vertices of a tetrahedron have the position vectors
then
the volume of the tetrahedron is

a)
b) 1
c) 2
d) none of these

86) The resolved part of the vector
along the vector
is and
that perpendicular to
is . Then

a)
b)
c)
d) All the above

87) A line passes through the point with position vector 3i-2j+5k and
is in the direction of 2i+2j-k, the equation of the line in the Cartesian
form is

a)
b)
c)
d)

88) The equation
represents a straight line passing through the points

a) (0,6,-1) and (1, -2,-1)
b) (0,6,-1) and ( -1,-4,2)
c) (1, -2, -1) and (1,4,-2)
d) (1,-2,-1) and ( 0,-6,1)

89) A vector
has length 21 and direction ratios 2,-3,6. The components of
(assume that
makes an acute angle with x-axis) are

a)
b)
c)
d) none of these

90)
a)
b)
c)
d)

91)
a)

a  =
1,   b  =  -1

b)

a  =
-1,   b  =   -1

c)

a  =
-1,   b  = 1

d)

a  =  1,   b  =  1

92) Which of the following expressions are meaningful ?
a)
b)
c)
d)

93)
a)
b)
c)
d)

94)
a)
b) 3/2
c) 2
d) 3

95)
a)
b)
c)
d)

96)
a)
b)
c)
d)

97)
a)
b)
c)
d)

98)
a) 1
b) 3
c)
d) None of the given

99)
a) 47
b) -25
c) 0
d) 25

100)
a) 0
b)
c)
d)