Vector Algebra MCQs Part II

1) The vectors 2i +3j-4k and ai+bj+ck are perpendicular when
a) a=2, b=3, c=-4
b) a=4, b=4, c=5
c) a=4, b=4, c=-5
d) none of these

2) The vectors A=3i-k, B=i+2j are adjacent sides of a parallelogram. Its
area is

a)
b)
c)
d)

3) If a and b position vectors of A and B respectively the position vector
of a point C on AB produced such that
is

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

4) The projection of the vector i-2j+k on the vector 4i-4j+7k is
a)
b)
c)
d)

5) If A=2i+2j+3k, B= – i+2j+k and C=3i+j, then A+tB is perpendicular to
C if t is equal to

a) 8
b) 4
c) 6
d) 2

6) If A= 2i+2j-k, B=6i-3j+2k then
will be given by

a) 2i-2j-k
b) 6i-3j+2k
c) i-10j-18k
d) i+j+k

7) The points with position vectors 10i+3j, 12i-5j, ai+11j are collinear
if a equal

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

8) The point with position vectors 60i+3j, 40i-8j, ai-52j are collinear if
a) a = -40
b) a = 40
c) a = 20
d) none of these

9) If
are three coplanar vectors, then

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

10)
a)
b)
c)
d) none of these

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

12) If =2i+4j-5k and =-i-2j+3k
then unit vectors parallel to
is

a)
b)
c)
d) none of these

13) The scalar product of
is equal to

a)
b)
c)
d) none of these

14) If are
two non-zero vectors and
is the angle between them then is
the vector

where

a)
b)
c)
d)

15) If
then

a)
b)
c)
d) none of these

16) If
a) (-1/7, 3/7)
b) (1/7, 3/7)
c) (1/7, -3/7)
d) (-1/7, -3/7)

17) Which of the following are not unit vectors?
a)
b)
c)
d) none of these

18) If =i+2j-3k
and =3i-j+2k
then

a)
b)
c)
d)

19) The area of the triangle, whose vertices are A (1, 2, 3),
B(2, -1, 1) and C(1, 2, -4) is

a)
b)
c)
d)

20) The area of the parallelogram whose adjacent sides are 3i+2j-k
and i+2j+3k is

a) 180 sq. uts
b)
c)
d) 204 sq. uts

21)
a)
b)
c)
d)

22) If
be three vectors, then

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

23)
a)
b)
c) 0
d) none of these

24)
a)
b)
c) 0
d)

25) The vector moment of three forces i+2j-3k, 2i+3j+4k and
-i-j+k acting on a particle at a point p(0, 1, 2)about the
point A(1, -2, 0) is

a) 140
b) 136
c)
d)

26) If A, B, C, D are any four points in space, then
a)
b)
c)
d) none of these

27)

For three vectors
which of the following expressions is not equal to
any of the remaining three ?


a)
b)
c)
d)

28) If
and are
linearly dependent vectors and
then

a)
b)
c)
d)

29) Which of the following expressions
are meaningful ?

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

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

a)
b)
c)
d)

31) The number of vectors of unit length
perpendicular to the vectors
and is

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

32) The values of x for which the angle
between the vectors
and is
acute, and the angle between the vector
and the axis of ordinates is obtuse , are

a) 1, 2
b) – 2, -3
c) all x < 0
d) Both (b) and (c)

33) The value of
a)
b)
c) 0
d) None of these

34) Let O be the circumcentre,
G be the centroid and O’ be the orthocentre of a Three
vectors are taken through O and are represented by
and then,
is

a)
b)
c)
d) None of these

35)
be three non-zero vectors, no two of which are collinear If the vector

a)
b)
c)
d)

36) If (x-y+2)I+(x+1)j is a null vector, then x and y are
a) 1, 1
b) -1, 1
c) -1, -1
d) 1, -1

37) A unit vector making an
obtuse angle with x-axis and perpendicular to the plane containing the points

a) also makes an obtuse angle with y-axis
b) also makes an obtuse angle with z-axis
c) also makes an obtuse angle with y and z axes
d) also makes an obtuse angle with y and z axes

38) are
two given vectors. On these vectors as adjacent sides a parallelogram is constructed.
The vector which is the altitude of the parallelogram and which is perpendicular
to

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

39)
a) all values of x
b)
c)
d) All the above

40) For
non-coplanar vectors

a)
b)
c)
d) None

41) If
the vector then
the unit vector in the direction of

a)
b)
c)
d)

42) If
satisfies
the equation then
for any scalar
is equal to

a)
b)
c)
d)

43) The
length of the longer diagonal of the parallelogram constructed on
and if
it is given that
and angle
between
and is

a) 15
b)
c)
d) None

44) The vector
is rotated through an angle
and doubled the magnitude, then it becomes
The value of x is

a)
b)
c) 2
d) Both (a) and (c).

45) If
are unit vectors such that vector
is perpendicular to
is perpendicular to

a)
b)
c)
d) None of these

46) If three vectorsand
the angle between

a) 4
b) – 4
c) 2
d) Both (a) and (b).

47) Let
a)
b)
c)
d)

48) Let
a)
b)
c)
d)

49) Let
be two non-collinear unit vectors. If

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

50)

If ABCD is a rhombus whose diagonals cut at the origin O, then


a)
b)
c)
d)

51) If ABCDEF is a regular hexagon
with

a)
b)
c)
d) none of these

52) Let ABCD be a parallelogram
whose diagonals intersect at P and let O be the origin , then

a)
b)
c)
d) None

53)
are the position vectors of A, B respectively and C is a point on AB produced
such that AC=3 AB, then the position vector of C is

a)
b)
c)
d)

54) Let
D, E, F be the middle points of the sides BC, CA, AB respectively of a triangle
ABC. Then

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

55) If
the vectors

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

56) The
vectors
have their initial points at (1,1). The value of
so that the vectors terminate on one straight line, is

a) 0
b) 3
c) 6
d) 9

57) If
a) coplanar
b) collinear
c) Non-collinear
d) None of these

58) If G is the centroid of a triangle ABC, then equals
a)
b)
c)
d)

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

a)
b)
c)
d)

60) Given that the vectors
are non-collinear
, the values of x and y for Which the vector equality holds
true if are

a)
b)
c)
d)

61)
a)
b)
c)
d)

62) The angle between the
vectors

a)
b)
c)
d) none of these

63) If the position vector
of the points are
then the three points are

a) collinear
b) non-coplanar
c) non-collinear
d) none of these

64) If
is equal to

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

65) If are
two unit vectors inclined at an angle such
that is
a unit vector then
is equal to

a)
b)
c)
d) None

66) The two vectorsare
parallel if

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

67) If
are three mutually perpendicular vectors each of magnitude unity then
is equal to

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

68)
a) 0, -2
b) 2, 0
c) 0, -1
d) 1, 0

69) The vectors
are perpendicular when

a) a=2, b=3, c=-4
b) a=4,b=4, c=5
c) a=4,b=4, c= -2
d) none of these.

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

71)

If
and
then
is perpendicular to
if t is equal to


a) 8
b) 4
c) 6
d) 2

72) Let
the pairs
each determines a plane. Then the planes are parallel if

a)
b)
c)
d)

73)
a)
b)
c)
d)

74) If
in a right angled triangle ABC, the hypotenuse AB=p, then

a)
b)
c)
d) none of these

75) If the vectors
are orthogonal to each other, then the locus of the point (x, y) is

a) a cricle
b) an ellipse
c) a parabola
d) a straight line

76)
then the angle between

a)
b)
c)
d)

77) The
vectors
form the sides of a triangle. This triangle is

a) an acute angled triangle
b) an obtuse angled triangle
c) a right angled triangle
d) an equilateral triangle

78) Let ABC be a triangle, the position vectors of whose vertices are respectively

a) isosceles
b) equilateral
c) right angled
d) Both ( c) and (a).

79)

A vector which makes equal angles with the vectors


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

80)
a) 1, 2
b) -2, -3
c) all x < 0
d) all x > 0

81)
a)
b)
c)
d) Both (a) and ( c).

82) The
area of a parallelogram whose diagonals coincide with the following pair of vectors
is then
vectors are

a)
b)
c)
d) none of these

83)
a) 1
b) 3
c)
d) none of these

84)
a)
b)
c)
d) Both (b) and ( c)

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

86)
a)
b)
c)
d)

87)
a)
b)
c)
d) none of these

88)
a)
b)
c)
d)

89)
a)
b)
c)
d)

90)
a) 225
b) 275
c) 325
d) 300

91)
a)
b)
c)
d) none of these

92)
a) 14
b) -14
c) 12
d) 15

93)
a) a=2, b=3, c=4
b) a=4, b=4, c=5
c) a=4, b=4, c=-5
d) none of these

94)
a)
b)
c)
d) none of these

95)
a)
b)
c)
d)

96)
a)
b)
c)
d)

97)
a) 7
b) 5
c) 13
d)

98)
a)
b)
c)
d) none of these

99)
equals

a) 10
b)
c)
d) 20

100)
a)
b)
c)
d) none of these

Answers

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