What is the area of the rectangle having vertices A, B, C and D with positive vectors `-hat(i)+(1)/(2) hat(j)+4hat(k), hat(i)+(1)/(2)hat(j)+4hat(k), hat(i)-(1)/(2) hat(j)+4hat(k) and -hat(1)-(1)/(2) hat(j)+4hat(k)`?

Options

A. 1/2 square unit
B. 1 square unit
C. 2 square unit
D. 4 square unit

Answer

C

Explanation

From the given vectors we can conclude that
`A(-1,1/2,4), B(1,1/2,4), C(1,-1/2,4), D(-1, -1/2,4)`
Length= AB=2, BC=1
Area `=ABxxBC=2`