The scalar  equals

a) 0

b)

c)

d) None of these

The volume of the parallelopiped whose sides are given by
 

a)

b) 4

c)

d) None of these

The points with position vectors  are collinear if

a)

b)

c)

d)

The number of unit vectors perpendicular to the vectors  and  is

a) 1

b) 2

c) 3

d) Infinitely many

e) None of these

Let a, b, c be three non co–planar vectors and p, q, r are vectors defined by the relations
  
Then the value of the expression
 is equal to

a) 0

b) 1

c) 2

d) 3

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

a) Arithmetic mean of a and b

b) Geometric mean of a and b

c) Harmonic mean of a and b

d) Equal to zero

Let p and q 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 ratio 2:3 respectively. If OR and OS are perpendicular then

a)

b)

c)

d)

Let α, β, γ 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

Let  If d is a unit vector such that  then d equals

a)

b)

c)

d)

Let are non–coplanar unit vectors such that

 then the angle between a and b is

a)

b)

c)

d) π

Let u, v and w be vectors such that  . If  then  is equal to

a) 47

b) –25

c) 0

d) 25

If a  are linearly dependent and |c|  then

a)

b)

c)

d)

Let  If c is a vector such that  and the angle between  and c is 30° then  is equal to

a)

b)

c) 2

d) 3

If the vectors  form sides BC, CA and AB respectively of a triangle ABC then

a)

b)

c)

d)

Let the vectors  be such that  . Let P₁ and P₂ be the planes determined by the pairs of vectors a, b and c, d respectively. Then the angle between P₁ and P₂ is

a) 0

b)

c)

d)

If   are unit vectors, then  does not exceed

a) 4

b) 9

c) 8

d) 6

The value of a so that the volume of parallelopiped formed by  becomes minimum is

a)  

b)  3

c)  

d)  

If a and b are two unit vectors such that  are perpendicular to each other then the angle between a and b is

a) 45°

b) 60°

c)

d)

Let  and u is a unit vector then the maximum value of  is

a)

b)

c)

d)

If  and  then b is equal to

a)

b)

c)

d)

If  are non-coplanar vectors and
  then a.b₁ and a.are orthogonal.

Let  . A vector in the plane of a and b whose projection on c is  is

a)

b) 3

c)

d)

The number of distinct real values of λ for which   are coplanar is

a) Zero

b) One

c) Two

d) three