Vector Algebra MCQs Part IV

1)

be three non-zero
vectors such that is a unit
vector perpendicular to both the vector
and . If the angle between
is
then,



a) 0
b) 1
c)
d)

2)

The value of c so that for all real x the vectors make an obtuse angle are


a) c<0
b) 0c) – 4/3 < c < 0
d) c>0

3) Letthen

a)
b)
c)
d)

4)

The vector satisfying
the conditions that




  1. it is

  2. it makes an obtuse angle with y-axis




a)
b)
c)
d) none of these

5) If
then x+y+z=

a)
b)
c)
d) none of these

6) Given two vectors
the unit vector coplanar with the two vectors and perpendicular to first is

a)
b)
c)
d) none of these

7) The vectors are
the adjacent sides of a parallelogram. Then angle between its diagonals is

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

8) The vector
is rotated through an angle
and doubled in magnitude, then it becomes
. The value of x is

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

9) If the vector bisects
the angle between the vector
and the vector
then the unit vector in the direction of is

a)
b)
c)
d)

10) If three vectors
are such that
and the angle between

a) 4
b) -4
c) -2
d) both a and b

11) For any vector
is equal to

a)
b)
c)
d) none of these

12) The vector
directed along the internal bisector of the angle between the vectors
and
is

a)
b)
c)
d)

13)

The value of x for which the angle between
is obtuse and the angle between
and the z-axis is acute and less than


a) ab) 1/2c) x>1/2 or x<0
d) none of these

14)

Let be
three vectors such that


a) 13
b) 81
c) 9
d) 5

15) Two planes are perpendicular to one another. One of them contains vectors

and the other contains vectors
then is
equal to

a) 1
b) 0
c)
d)

16) If the non-zero vectors
are perpendicular to each other, then the solution of the equation

a)
b)
c)
d)

17) The three vectors
a) an equilateral triangle
b) a right angled triangle
c) an isosceles triangle
d) collinear vectors

18) For a non-zero vector ,
the set of all real numbers satisfying the inequality
consists of all x such that

a) 0b) 3 < x < 7
c) -7 < x < -3
d) -7 < x < 3

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

20) Let be
three vectors. A vector in the plane of
whose projection on
is of magnitude

a)
b)
c)
d)

21) Let a,b,c be distinct non-negative numbers. If the vectors
lie in a plane, then c is

a) the A.M. of a and b
b) the G.M of a and b
c) The H.M of a and b
d) Equal to zero

22) Let
be two vectors perpendicular to each other in the xy-plane. Then a vector in
the same plane having projections 1 and 2 along
respectively is

a)
b)
c)
d) none of these

23) The vector
is to be written as the sum of a vector ,
parallel to
equals

a)
b)
c)
d)

24) If
are three non-coplanar vectors then
equals

a) 0
b)
c)
d)

25) A vector
has magnitude 5 units and points north east and another vector
has magnitude 5 units and points north west. Then the magnitude of the vector
is

a) 0
b)
c) 10
d) 25

26)

If I is the centre of a circle inscribed in a triangle ABC, then



is



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

27) Let
be three non-zero vectors, no two of which are collinear. If the vector
is collinear with and
is collinear with
then
is equal to

a)
b)
c)
d) 28) The value of x for which the angle between the vectors
is acute, and the angle between the vector
and the axis of co-ordinates is obtuse are

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

29) 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 acute angle with y and z axis
d) also makes an obtuse angle with y and z-axis

30) If the vectors
make an obtuse angle for any

a)
b)
c) (-4/3,0)
d) None

31) If
are unit vectors such that
then the value of

a) 1
b) 3
c) -3/2
d) none of these

32) The vectors are
coplanar for

a) all values of x
b) x<0
c) x>0
d) all the above

33) If
satisfying the conditions
(i). That it is coplanar with
(ii). That it is perpendicular to
(iii). That is

a)
b)
c)
d) none of these

34) If are unit orthonormal vectors and is a vector, if then
a) 0
b) 1
c) -1
d) arbitrary scalar

35) A unit vector in the xy-plane makes as angle of
with the vector
and an angle of
with the vector is

a)
b)
c)
d) none of these

36) Let
and a unit vector
be coplanar. If
is perpendicular to

a)
b)
c)
d)

37) Let .
If
is a vector such that
and the angle between

a) 283
b) 3/2
c) 2
d) 3

38)

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



a)
b)
c)
d) none of these

39) 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)

40) If
are linearly independent vectors and
then

a)
b)
c)
d) none of these

41) 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

42) If the vector
are three non-coplanar vector and =0
then the value of abc is

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

43) Each of the angle between vectors
and
is equal to
If
then the modulus of

a) 10
b) 15
c) 12
d) none of these

44) Let
represent respectively
where ABC is a triangle. Then

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

45) If the vectors
are coplanar, then the value of
is

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

46)

In a right angled triangle ABC the hypotenuse AB=p, then



is equal to


a)
b)
c)
d) none of these

47) equal
to

a) [abc]
b) 2[abc]
c) 3[abc]
d) 0

48) Vectors
and
are inclined at an angle
then is equal
to

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

49) The projection of the vector
on the axis making equal acute angles with the co-ordinate axes is

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

50)
is equal to

a)
b)
c)
d) none of these

51) The three vectors
taken two at a time form three planes. The three vectors drawn perpendicular
to three planes form a parallelopiped of volume(cubic units)

a) 1/3
b) 4
c)
d) none of these

52) Let
be unit vectors such that .
If the angle between
is

a)
b)
c)
d)

53) 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

54) If
then

a)
b)
c)
d) none of these

55) A force of 39 kg wt. Is acting at a point P(-4,2,5) in the direction .
The moment of this force about a line through the origin having the direction
of
is

a) 76 units
b) -76 units
c) 56 units
d) none of these

56) 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
and
is.

a)
b)
c)
d) none of these

57) The centre of the circle given by
and
is

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

58) A vector
is equally inclined with the coordinate axes. If the tip of
is in the positive octant and ,
then
is

a)
b)
c)
d)

59) If
is a vector of magnitude 21 and had DRs 2, -3, 6, then
is equal to

a)
b)
c)
d)

60) The position vectors of two points P and Q are
and respectively.
The equation of the plane through Q and
to PQ is

a)
b)
c)
d) none of these

61) The vector equation of the plane passing through the origin and the line
of intersection of the plane
and
is

a)
b)
c)
d)

62) The position vectors of points A and B are
and
respectively. The equation of a plane is
The points A and B

a) lie on the plane
b) are on the same side of the plane
c) are on the opposite sides of the plane
d) none of these

63) The vector equation of the plane through the point
and parallel to the plane
is

a)
b)
c)
d) none of these

64) The vector equation of the plane through the point
and
to the line of intersection of the plane
and
is

a)
b)
c)
d) none of these

65) The vector equation of a plane which contains the line
and
to the plane
is

a)
b)
c)
d) none of these

66) The equation of the plane containing the lines
and
is

a)
b)
c)
d) none of these

67) The equation of the plane containing the lines
a)
b)
c)
d) none of these

68) The line of intersection of the planes
is parallel to the vector

a)
b)
c)
d)

69) The vector equation of the plane containing the lines
a)
b)
c)
d) none of these

70) The Cartesian equation of the plane
a)
b)
c)
d)

71) The distance between the line
a)
b)
c)
d) none of these

72) The vector equation of the line of intersection of the planes
a)
b)
c)
d) none of these

73) A straight line
meets the plane
The position vector of P is

a)
b)
c)
d) none of these

74) The length of the perpendicular from the origin to the plane
passing through three non-collinear points
is

a)
b)
c)
d) none of these

75) The length of the perpendicular from the origin to the plane
passing through the point
and containing the line

a)
b)
c)
d)

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

a)
b)
c)
d)

77) The line joining the points
and the line joining the points
intersect at

a)
b)
c)
d) none of these

78) Angle between the line
a)
b)
c)
d)

79) The line through
a)
b)
c)
d)

80) The distance from the point
to the straight line through the point (2,3,-4) and
parallel to the vector

a) 7
b) 10
c) 9
d) none of these

81) The position vector of the point in which the line
joining the points
cuts the plane through the origin and the points

a)
b)
c)
d) none of these

82) will intersect if

a)
b)
c)
d) none of these

83) The distance between the planes given by
a) 1 unit
b)
c) 13 units
d) none of these

84) The vector equation of the plane through the point (2, 1, -1) and passing
through the line of intersection of the plane
and ,
is

a)
b)
c)
d) none of these

85) The equation of the plane containing the line
a)
b)
c)
d) none of these

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

a)
b)
c)
d) none of these

87) The equation
represents a

a) circle
b) plane
c) sphere of radius 4
d) sphere of radius 3

88) The vector equation of the plane through the point 2i -j – 4 k and parallel
to the plane r. (4i-12j-3k) -7= 0 is

a) r.(4i-12j-3k) = 0
b) r. (4i-12j-3k) = 32
c) r. (4i-12j-3k) = 12
d) r.(2i-j-4k ) = 12

89) The angle between the line
and the plane

a)
b)
c)
d)

90) The perpendicular distance of the point (2, 1, 4) from the plane

a) 2
b)
c) 3
d)

91) A vector P is inclined at equal angles to ox, oy and oz. If the magnitude
of P is 9 units, then P=

a) 3i+ 3j-3k
b)
c)
d) None of these

92) The Cartesian equation of a line is
. The vector equation of the line is

a)
b)
c)
d) None of these

93) The equation of the plane which is at a distance
of 10 units from the origin and is perpendicular to
3i+2j-5k, directed away from the origin is

a) 3x+2y-5z=0
b) x+3y-5z=10
c)
d) None of these

94) The position vector of two points A and B are 2i+
2j+k and i-j+3k respectively. The equation of the
plane through B and perpendicular to AB is

a) x-3y -2z-8=0
b) x+3y +2z=8
c) x+3y -2z+8=0
d) x+3y +2z+8=0

95) The Angle between the planes r(3i-j+k)=1 and r(i+j+k)=2
is

a)
b)
c)
d)

96) A line passing through the point (3,-1,-2) and perpendicular
to the plane r(3i-2j+3k)=6. The point of intersection
of the line and the plane is

a)
b)
c)
d) None of these

97) The magnitude of the moment of force
acting at the point
about the point
is

a)
b) 0
c)
d)

98) The following pair of
lines



a) intersect
b) do not intersect
c) coplanar
d) none of these

99) The equation of the
plane through the point
and perpendicular to the line of intersection of the planes

a)
b)
c)
d) none of these

100) The line,
will intersect if

a)
b)
c)
d) none of these

Answers

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