# 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)**

**Answers**