Thus,
Area of parallelogram ABCD =  |
||
| sin
b
a
θ
r
r
 
|
| a
b
=
×
r
r
We now state two important properties of vector product Property 3 (Distributivity of vector product over addition): If ,
a band
c
rr
r
are any three vectors and λ be a scalar, then
(i)
(
)
a
b
c
×
r+
r
r  = a
b
a
c
 
 
r
r
r
r
(ii)
(
λa b)
×
r
r
 = (
)
(
)
a
b
a
b
λ
×
=
× λ
r
r
r
r
Fig 10 26
 Fig 10