NDA 2 2025 Maths, question 55

Topic: Analytical geometry

Passage · Q55 to Q56

Let $A(1,-1,0)$ , $B(-2,1,8)$ and $C(-1,2,7)$ are three consecutive vertices of a parallelogram $ABCD$ .

Q55

What is the fourth vertex $D$ ?

(a) $(0,-2,1)$
(b) $(2,0,-1)$ Correct answer
(c) $(1,0,1)$
(d) $(1,2,0)$

Solution.

Answer: (b) $(2,0,-1)$

Diagonals of a parallelogram bisect each other, so A+C=B+D.
Hence D=A+C−B=(2,0,−1).
Also AD=(1,1,−1)=BC, confirming the vertex order.