(iii)
In case if it is given that  l, m, n are direction cosines of a vector, then 
ˆ
ˆ
ˆ
li
mj
nk
+
+
= 
ˆ
ˆ
ˆ
(cos )
(cos )
(cos )
i
j
k
α
+
β
+
γ
 is the unit vector in the direction of that vector,
where α, β and γ are the angles which the vector makes with x, y and z axes
respectively Example 4 Find the values of x, y and z so that the vectors 
ˆ
ˆ
2ˆ
a
xi
j
zk
=
+
+
r
 and
ˆ
ˆ
ˆ
2
b
i
yj
k
=
+
+
r
 are equal Solution Note that two vectors are equal if and only if their corresponding components
are equal Thus, the given vectors 
aand 
rb
r
 will be equal if and only if
x = 2, y = 2, z = 1
© NCERT
not to be republished
 MATHEMATICS
436
Example 5 Let 
ˆ
2ˆ
a
i
j
r= +
 and 
ˆ
ˆ
2
b
i
j
=
+
r