Find the area of the parallelogram that has adjacent sides v = i-2j+3k and w=i-3j-2k

Question

The area of the parallelogram is ?

Answer 1

The area, A, of a parallelogram is:

A = product of the lengths of the adjacent sides times the sine of the angle between them

It is easy to work out the the lengths of v and w are both sqrt(14).

The cosine of the angle between v and w can be obtained from the dot product formula

cos(θ) = v • w /( product of magnitudes) = 1/14

The sine is therefore sqrt( 1 - 14^2)

and A = 14 sqrt(1 - 14^2) = sqrt(195)