Show that the direction cosines of a vector equally inclined to the axes OX, OY
and OZ are 1
1
1
,
, 3
3
3
12 Let 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
4
2 ,
3
2
7   and  
2
4
a
i
j
k b
i
j
k
c
i
j
k
= +
+
=
−
+
=
−
+
r
r
r Find a vector d
r
which is perpendicular to both 
a and 
rb
r
, and 
15
c d
⋅
rr=