NDA 1 2025 Maths, question 62

Topic: Analytical geometry

Q62

$A(1,2, - 1)$ , $B(2,5, - 2)$ and $C(4,4, - 3)$ are three vertices of a rectangle. What is the area of the rectangle?

Solution.

Answer: (c) $\sqrt{66}$ square units

The vectors $\overrightarrow{AB} = (1,3, - 1)$ and $\overrightarrow{BC} = (2, - 1, - 1)$ have dot product $2 - 3 + 1 = 0$ , so the right angle is at $B$ .
The adjacent side lengths are $\sqrt{11}$ and $\sqrt{6}$ .
Their product gives the area $\sqrt{66}$ square units.