14 If ,
a b, c
r r
r
 are mutually perpendicular vectors of equal magnitudes, show that
the vector a
b
c
+
r+
r
r  is equally inclined to ,
and
a
b
c
r
r
r © NCERT
not to be republished
VECTOR ALGEBRA
459
15 Prove that  
2
2
(
) (
) |
|
| |
a
b
a
b
a
b
+
⋅
+
=
+
r
r
r
r
r
r
, if and only if ,a b
rr
 are perpendicular,
given 
0,
0
a
b
≠
rr≠
r
r