Question.1
Let 
and 
be two unit vectors such
that + is also a unit vector .
The angle between and 
is
(A) 30°
(B) 60°
(C) 90°
(D) 120°
Solution
Let q be the angle between 
and 
+ will be a unit vector
if and only if 
i.e. .= – 1/2 or cosq = – 1/2 or q = 1200
Question.2
are two vectors
such that 
=
. Then;
(A) ∠BOA = 90°
(B) ∠BOA > 90°
(C) ∠BOA < 90°
(D) 60° £ ∠BOA
£ 90°
Solution
Given
=
.
On squaring (OA)2 +(OB)2 +2
=
(OA)2 + 4(OB)2 +4
&⇒ 2= - 3
< 0
&⇒ 2 
&⇒ cosq
< 0
&⇒ q >
90°
i.e. ∠
BOA > 90°.
Question.3
If for non zero vectors 
then
(A) is
perpendicular to the plane of and 
(B) is
parallel to the plane of and
(C) is
perpendicular to and parallel to
(D) None of these
Solution
&⇒ 
&⇒ is
collinear with 
&⇒is parallel to the
plane of 
Question.4
If 
are two
unit vectors and q is the angle between them, then the unit
vector along the angular bisector of will be
given by
(A) 
(B) 
(C) 
(D) none of these. .
Solution
vector in the
direction of angular bisector of 
= 
.
have magnitude
cos(q/2)
so, the unit vector in this direction will have
magnitude 
.
Question.5
A unit vector in xy – plane which makes an angle of 45°
with the vector 
and an angle of
60° with the vector 
is
(A) 
(B) 
(C) 
(D) None of these
Solution
Let 
&⇒ a2
+ b2 = 1 …(1)
Also,
cos45° = 
&⇒ a
+ b = 1 …(2)
cos60° = 
&⇒ 3a
– 4b = 
…(3)
There exists no real values of a and b satisfying (1),
(2) and (3).
Hence no such unit vector exists.
Question.6
If 
where |
| = 1 " i,
then the value of 
is
(A) –n/2
(B) –n
(C) n/2
(D) n
Solution
=
0
.= 
&⇒ 0
= n + 2
&⇒= 
Question.7
Find the angle
between the two straight lines 
and 
.
(A) 
(B) 
(C) 
(D) 
Solution
The first line
parallel to the vector 
The second line
parallel to the vector 
If q is the angle between the lines then,
= 
\ 
.
Question.8
If 
, then 
´[
´
]is equal to
(A) A vector perpendicular to plane of 
(B) A scalar quantity
(C) 
(D) None of these
Solution
&⇒
Vectors 
are coplanar
&⇒ 
and 
are collinear
&⇒ 
.
Question.9
If r, a, b, c are
non null vectors such that 
, then 
(A) is equal to 1
(B) cannot be
evaluated
(C) is equal to
zero
(D) none of these
Solution
Since 
= 0, 
and 
, 
must be perpendicular to
all the three vectors 
. Hence must be coplanar
&⇒ 
=0
Question.10
Let 
and 
. If is a vector such that 
=
and the angle between 
and is 300, then
find the value of 
.
(A) 2/3
(B) 3/2
(C) 2
(D) 3
Solution
= 
sin 300
&⇒ 
=
8
&⇒ 
= 8
&⇒ 
&⇒ 
&⇒ = 1. 3. 
= 
