Question

If (1, 2, –1), (2, 3, 0) and (–3, 1, –2) are three vertices of a parallelogram then fourth vertex may be

• A. (–2, 2, –1)
• B. (–4, 0, –1)
• C. (6, 4, –1)
• D. (2, –3, 0)

Answer 1

The correct option is A (–2, 2, –1)

If A,B,C and D are consecutive vertices of a parallelogram
then D = A+C–B
Here A = (1,2,-1), B = (2,3,0), C = (–3,1,–2)
Since these are not consecutive vertices, fourth vertex will be either of A+B–C (or) A+C–B (or) B+C–A
i.e A+B –C = (6, 4, 1)
A+C –B = (–4, 0, –3)
B+C –A = (–2, 2, –1)