# Vector Algebra MCQs Part III

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

**2) ****a)** **b)** **c)** **d)**

**3) ****a)** **b)** **c)** **d)**

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

**5) If ****a)** 7**b)** 5**c)** 13**d)**

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

**7) ****a)** **b)** **c)** **d)**

**8) ****a)** – 4**b)** -1**c)** 4**d)** – 2

**9) ****a)** -1

**b)** 0**c)** 1**d)** Both (a) and (c)

**10) ****a)** 2**b)** 3**c)** 0**d)** none of these

**11) For any three vectors ****a)** **b)** **c)** **d)** none of these

**12) ****a)** **b)** **c)** **d)**

**13) For any three vectors ****a)** **b)** **c)** **d)**

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

**15) ****a)** 0**b)** **c)** **d)**

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

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

**18) ****a)** 0**b)** 1**c)** **d)**

**19) ****a)** **b)** **c)** **d)**

**20) ****a)** p=0**b)** **c)** **d)** p=1 or p= -1

**21) If are
non-coplanar vectors, then **

**a)**

**b)**

**c)**

**d)**none of these

**22)
equals **

**a)**

**b)**

**c)**

**d)**none of these

**23) ****a)** **b)** **c)** **d)** none of these.

**24) ****a)** **b)** **c)** **d)**

**25) If
the constant forces
act on a particle due to which it is displaced from a point then
the work done by the forces is
**

**a)**15 units

**b)**-15 units

**c)**9 units

**d)**-9 units

**26) The work done by the force
in moving an object along the vector **

**a)**-9 units

**b)**15 units

**c)**9 units

**d)**none of these

**27) If forces of magnitudes 6 and
7 units acting in the directions
respectively act on a particle which is displaced from the point ,
then the work done by the forces is**

**a)**4 units

**b)**-4 units

**c)**7 units

**d)**-7 units

**28) If
the force represented by
is acting through the point
then its moment about the point
is **

**a)**

**b)**

**c)**

**d)**

**29) The
moment of the couple formed by the forces
respectively is**

**a)**

**b)**

**c)**

**d)**

**30) A force of 39 kg.wt is acting
at a point
The moment of this force about a line through the origin having the direction
of
is**

**a)**76 units

**b)**-76 units

**c)**

**d)**none of these

**31) A,
B have position vectors
relative to the origin O and X, Y divide
internally and externally respectively in the ratio 2 : 1. **

**a)**

**b)**

**c)**

**d)**

**32) ****a)** **b)** **c)** **d)** none of these

**33) The
projection of the vector
on the axis making equal acute
angles with the coordinate axes is**

**a)**3

**b)**

**c)**

**d)**none of these.

**34) If
is vector of magnitude 50 collinear with the vector
and makes an acute angle with
the positive direction of z-axis, then**

**a)**

**b)**

**c)**

**d)**none of these

**35) ****a)** 11**b)** -11**c)** 33**d)** -33

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

**a)**

**b)**

**c)**

**d)**none of these

**37) Consider
a tetrahedron with faces
be the vectors whose magnitudes are respectively equal to areas of
and whose directions are perpendicular to these faces in outward direction. Then
equals **

**a)**1

**b)**4

**c)**0

**d)**none of these

**38) A
vector which makes equal angles with the vectors **

**a)**

**b)**

**c)**

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

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

**a)**AM of a and b

**b)**GM of a and b

**c)**HM of a and b

**d)**none of these

**40) If
a vector
is directed along the bisector of the angle between the vectors **

**a)**

**b)**

**c)**

**d)**Both (a) and (c)

**41) If
the vectors are
inclined at an acute angle, then **

**a)**a = 0

**b)**a < 0

**c)**a > 0

**d)**none of these

**42) If
are three non-zero vectors such that ,
then **

**a)**m < 0

**b)**m > 0

**c)**m = 0

**d)**m = 3.

**43) Let
be three vectors. A vector in the plane of
whose projection on **

**a)**

**b)**

**c)**

**d)**Both (a) and (c)

**44) Let
are three non-coplanar vectors such that **

**a)**

**b)**

**c)**

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

**45) If
are three non-coplanar vectors such that **

**a)**

**b)**

**c)**

**d)**

**46) ****a)** **b)** **c)** **d)**

**47) Let
be three non-zero vectors such
that no two of which are collinear
and the vector
**

**a)**

**b)**

**c)**

**d)**none of these

**48) A
parallelogram is constructed on the vectors
then the length of a diagonal of the parallelogram is**

**a)**

**b)**

**c)**

**d)**none of these

**49) ****a)** 47**b)** -25**c)** 0**d)** 25

**50) If are
three non-coplanar vectors, then
equals**

**a)**0

**b)**

**c)**

**d)**

**51) If
are non-coplanar unit vectors such that **

**a)**

**b)**

**c)**

**d)**

**52) 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

**53) Let
be the position vectors of P and Q respectively, with respect to O and
The points R and S divide PQ internally and externally in the ration 2:3 respectively.
If are
perpendicular, then**

**a)**

**b)**

**c)**

**d)**

**54) The vector
is **

**a)**unit vector

**b)**

**c)**

**d)**All the above.

**55) ****a)** **b)** **c)** **d)**

**56) The
number of vectors of unit length
to the vectors **

**a)**one

**b)**two

**c)**three

**d)**infinite

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

**58) The vector
lies in the plane of vectors
which of the following is correct **

**a)**

**b)**

**c)**

**d)**

**59) A unit vector perpendicular
to **

**a)**

**b)**

**c)**

**d)**none of these

**60) 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)**none of these

**61) ****a)** **b)** **c)** **d)** 0

**62) **

are three non-coplanar vectors, then the value of the expression

**a)**3

**b)**2

**c)**1

**d)**0

**63) **

**The points with position vectors
are collinear if**

**a)**a = -40

**b)**a = 40

**c)**a = 20

**d)**none of these

**64) The
points with position vectors
are collinear if the value of a is**

**a)**-8

**b)**4

**c)**8

**d)**12

**65) If
C is the middle point of AB and P is any point outside AB, then**

**a)**

**b)**

**c)**

**d)**

**66) The
value of b such that the scalar product of the vector
with the unit vector parallel
to the sum of the vectors **

**a)**-2

**b)**-1

**c)**0

**d)**1

**67) ****a)** 12**b)** 2**c)** 0**d)** -12

**68) ****a)** 16**b)** 8**c)** 3**d)** 12

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

**a)**c < 0

**b)**

**c)**

**d)**c > 0

**70) ****a)** 6**b)** 5**c)** 4**d)** 3

**71) The median AD of the triangle
ABC is bisected at E, BE meets AC in F, then AF: AC =
**

**a)**

**b)**

**c)**

**d)**

**72) If the vectors
and
are coplanar, then x =**

**a)**

**b)**

**c)**0

**d)**1

**73) Volume of the parallelopiped
whose coterminal edges are
is **

**a)**5 units

**b)**6 units

**c)**7 units

**d)**8 units

**74)
is not perpendicular to **

**a)**

**b)**

**c)**

**d)**

**75) If
are unit orthonormal vectors and
is a vector, if
then
is **

**a)**0

**b)**1

**c)**-1

**d)**arbitrary scalar

**76) 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

**77) **

is equal to

**a)**

**b)**

**c)**

**d)**0

**78) **

**In the trapezoid the vector
We will then find that **

**a)**

**b)**

**c)**

**d)**

**79) **

**The vector
is perpendicular to the vectors and
satisfying the condition **

**a)**

**b)**

**c)**

**d)**none of these

**80) ****a)** **b)** **c)** **d)**

**81)
be any three non-zero non-coplanar vectors, then any vector ,
is equal to
**

**a)**

**b)**

**c)**

**d)**none of these

**82) **

**The vector
coplanar with the vectors
perpendicular to the vector **

**a)**

**b)**

**c)**

**d)**none of these

**83) ****a)** **b)** **c)** **d)** none of these

**84) A unit vector in xy-plane makes
an angle of**

**a)**

**b)**

**c)**

**d)**none of these

**85) ****a)** 1**b)** **c)** 0**d)** none of these

**86) ****a)** **b)** **c)** **d)** None of these

**87) If are unit vectors and is
the angle between them, then
**

**a)**

**b)**

**c)**

**d)**

**88) If ****a)** **b)** **c)** **d)** none of these

**89) If ****a)** **b)** **c)** **d)**

**90) The vectors and
include an acute angle for **

**a)**all real m

**b)**m<-2 or m>-1/2

**c)**m=-1/2

**d)**

**91)
**

**a)**0

**b)**1

**c)**2

**d)**3

**92) Three numbers form an increasing G. P. If the middle
number be doubled, then the new numbers are in A.
P. the common ratio of the G. P is**

**a)**

**b)**

**c)**

**d)**

**93) ****a)** 0**b)** **c)** **d)**

**94) The length of the longer diagonal of the parallelogram whose adjacent
sides are along
and
angle between **

**a)**

**b)**

**c)**

**d)**

**95) The number of vectors of unit length perpendicular to the vectors
**

**a)**1

**b)**2

**c)**4

**d)**infinite

**96) The value of ****a)** **b)** **c)** 0**d)** none of these

**97) For non-coplanar vectors ****a)** **b)** **c)** **d)**

**98) If
are unit vectors such that the vector
is perpendicular to
is perpendicular to
then the angle between**

**a)**

**b)**

**c)**

**d)**

**99) ****a)** **b)** **c)** **d)**

**100) Let then
satisfying **

**a)**

**b)**

**c)**

**d)**

**Answers**