NDA 2 2025 Maths, question 66

Topic: Vectors

Q66

Let $\overrightarrow{p}=\overrightarrow{a}-\overrightarrow{b}$ , $\overrightarrow{q}=\overrightarrow{a}+\overrightarrow{b}$ . If $|\overrightarrow{a}|=|\overrightarrow{b}|=2$ and $\overrightarrow{a}\cdot \overrightarrow{b}=2$ , then what is the value of $|\overrightarrow{p}\times \overrightarrow{q}|$ ?

(a) $\sqrt{3}$
(b) $\sqrt{6}$
(c) $2\sqrt{3}$
(d) $4\sqrt{3}$ Correct answer

Solution.

Answer: (d) $4\sqrt{3}$

(a−b)×(a+b)=2(a×b).
Also |a×b|²=|a|²|b|²−(a·b)²=16−4=12.
Thus |p×q|=2√12=4√3.