The area of the rectangle having vertices P , Q , R , S with position vectors - i + j + k , i + j + k , i - j + k ,- i - j + k respectively is

Step-by-step solution

Position vectors in 3D space: Given vertices: P = - i + j + k , Q = i + j + k , R = i - j + k , S = - i - j + k Adjacent sides from vertex P: PQ = Q - P = 2 i , PS = S - P = -2 j These vectors are orthogonal with magnitudes | PQ | = 2 and | PS | = 2 , confirming rectangular geometry. The area follows from the cross product magnitude or product of adjacent sides: | PQ PS | = |(2 i ) (-2 j )| = 4 4 square units