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” The germinal ideas of modern vector theory date from around 1800
when Caspar Wessel (1745-1818) and Jean Robert Argand (1768-1822) described
that how a complex number a + ib could be given a geometric interpretation with
the help of a directed line segment in a coordinate plane William Rowen Hamilton
(1805-1865) an Irish mathematician was the first to use the term vector for a
directed line segment in his book Lectures on Quaternions (1853)