a parrallelogram has adjacent sides given by

 

A= 5 i^ - 4 j^  + 3 k^

B= 3i^ + 2 j^  - k^

 

Find the area of parallelogram.

hurry plz,,,,

to find the area of the parallelogram encompassed by two vectors, just take the cross product of the two vectors and find it's magnitude. the value of the magnitude will give you the area.

 

This is because:

|a x b|=|a| |b| Sin(A) where a is the angle between the two vectors.

also |b| Sin(A) is the value of the perpendicular projection of 'b' vector on 'a' vector, therefore |a| |b| Sin(A) is equivalent to the area of the parallelogram area formula (base)*(perpendicular projection or altitude).

Hence, the area.