Question

Find the vector area and the area of the parallelogram having a = i +2j - k and
b = 2i - j + 2k as adjacent sides,​

Answer 1

Answer:

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