# 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

**Answers**