- If Ѳ is the angle between the
vectors and ⃗^ , such that | ⃗^ |
| ⃗^ |, then Ѳ is:
(a) 0 (b) 45 (c) 120 (d) 180
- If , ⃗^ , are three mutually
perpendicular vectors each of unit
magnitude, then what is the magnitude
of ⃗^?
(a) 3 (b) 1 (c) √ (d) 1/3
- ⃗⃗⃗^ are vectors of length 3, 4 and
5 respectively such that is
perpendicular to ( ⃗^ ), ⃗^ to ( )
and to ( ⃗^ ). What is the
magnitude of the vector ⃗^?
(a) 12 (b) 2√ (c) 5√ (d) 50
If | ⃗^ |
= k | ⃗^ |
| |^ | |^ , then
what is the value of k?
(a) 1 (b) 2 (c) 0 (d) - 1
If α, β and γ are distinct non-
negative real numbers such that the
vectors ̂ ̂ ̂ ̂ ̂ and
β ̂ ̂ ̂ are coplanar, then which
one of the following is correct?
(a) (b) β =^ (c) β = (d)
α= 1, β= 0, γ= 1
- If ⃗^ are the position vectors of
corners A, B, C of a parallelogram
ABCD, then what is the position vector
of the corner D?
(a) ⃗^ (b) ⃗^ (c)
⃗^ (d) - ⃗^
35. If two unit vectors and make an
angle^ with each other, what is the
magnitude of?
(a) 0 (b) √ (c) 1 (d) √^36. What are the values of x for which
the two vectors ( ) ̂ ( ) ̂
̂ and 2 ̂ ̂ ̂ are orthogonal?
(a) No real value of x (b) x=^ and x= - 1
(c) x= - and x= 1 (d) x= -1 and x= 237. A particle is acted upon by
following forces:
(i) 2 ̂ ̂ ̂ (ii) - 5 ̂ ̂ ̂ and
(iii) 3 ̂ ̂
In which plane does it move?
(a) x-y plane (b) y-z plane (c) z-x plane
(d) Any arbitrary plane
38. If ⃗⃗⃗ , ⃗⃗⃗ ⃗⃗⃗ are the position vectors
of three collinear points and scalars m
and n exist such that ⃗⃗⃗ ⃗⃗⃗ ⃗⃗⃗ ,
then what is the value of (m + n)?
(a) 0 (b) 1 (c) -1 (d) 2- A force m ̂ ̂ ̂ acts on a point
and so the point moves from (20, 3m,
- to (0, 0, 7). If the work done by the
force is -48 units, what is the value of
m?
(a) 5 (b) 3 (c) 2 (d) 1
41. If a and b are two vectors such that
a.b= 0 and a × b= 0, which one of the
following is correct?
(a) a is parallel to b (b) a is
perpendicular to b (c) Either a or b is a
null vector (d) None of the above