# 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**