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