Such
that 
ˆ
, ,
r
ra b n form right handed system of coordinate axes � If we have two vectors 
aand
rb
r
, given in component form as
1
2
3 ˆ
ˆ
ˆ
a
a i
a j
a k
=
+
+
r
 and 
1
2
3 ˆ
ˆ
ˆ
b
b i
b j
b k
=
+
+
r
 and λ any scalar,
© NCERT
not to be republished
VECTOR ALGEBRA
461
then
a
b
+
r
r
 =
1
1
2
2
3
3 ˆ
ˆ
ˆ
(
)
(
)
(
)
a
b i
a
b
j
a
b
k
+
+
+
+
+
;
a
λr  =
1
2
3 ˆ
ˆ
ˆ
(
)
(
)
(
)
a i
a
j
a k
λ
+ λ
+ λ
;
rr a b
 =
1 1
2 2
3 3
a b
a b
a b
+
+
;
and
a
b
×
r
r
 =
1
1
1
2
2
2
ˆ
ˆ
ˆ i
j
k
a
b
c
a
b
c
Historical Note
The word vector has been derived from a Latin word vectus, which means
“to carry”