Question

Find the area of the parallelogram whose adjacent sides are i + 2j + 2k and 2i + j - k.

Answer 1

Let ABCD be the parallelogram whose sides are

vector(AB - a) = i + 2j + 2k and vector BC = vector b = 2i + j - k

Now, vector(a x b) = |(i,j,k),(1,2,2),(2,1,-1)|

= i(-2 - 2) - j(-1 - 4) + k(1 - 4) = -4i + 5j - 3k

So, area of parallelogram

ABCD = vector|a x b| = |-4i + 5j - 3k| = √50 

5√2 sq. unit