Examples
Ex 1:
What is the area of the parallelogram spanned by the vectors
= 3
– 3
+
and 
= 4+ 9+2 ?
Sol:
| × |
= |  |
| = | (– 6 – 9) – (6 – 4) + (27 + 12) |
|
| = | – 15 – 2+ 39 |
|
| Area of the parallelogram | = | | × | |
| = | |– 15 – 2 + 39| |
|
| = |  |
|
| = | 5√70 sq.units. |
Ex 2:
Find the vector area and the area of the parallelogram whose adjacent sides are
a = i + 2j – k, b = 2i – j + 2k
Sol:
| a × b | = |  |
| = | i(4 – 1) – j(2 + 2) + k(– 1 – 4) = 3i – 4j – 5k | |
| Vector area of the parallelogram | = | 3i – 4j – 5k |
| Area of the parallelogram | = | | 3i – 4j – 5k | |
| = | √(9 + 16 + 25) | |
| = | 5√2 sq.unit. |