Two particles are located at equal distance from origin. The position vectors of those are represented by A = 2i + 3nj + 2k and B = 2i - 2j + 4pk, respectively. If both the vectors are at right angle to each other, the value of n⁻¹ is ________. Numerical answer type. Work it out, then open the answer.

Answer: 3. Equal distance: 4 + 9n² + 4 = 4 + 4 + 16p² ⇒ 9n² = 16p², p = ±3n/4. Perpendicular: A · B = 4 - 6n + 8p = 0. p = +3n/4 gives 4 = 0 (impossible); p = -3n/4 gives 4 - 12n = 0 ⇒ n = 1/3. Answer: n⁻¹ = 3

Two particles are located at equal distance from origin. The position… | JEE Main 2025 (23 Jan, Shift 1)

Q15JEE Main 2025 · 23 JAN · SHIFT 1Medium

Scalar (Dot) Product

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} - 2\hat{j} + 4p\hat{k}$ , respectively. If both the vectors are at right angle to each other, the value of $n^{-1}$ is ________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 3

Equal distance: $4 + 9n^2 + 4 = 4 + 4 + 16p^2 \Rightarrow 9n^2 = 16p^2,\ p = \pm\frac{3n}{4}$ .
Perpendicular: $\vec{A} \cdot \vec{B} = 4 - 6n + 8p = 0$ .
$p = +\frac{3n}{4}$ gives $4 = 0$ (impossible); $p = -\frac{3n}{4}$ gives $4 - 12n = 0 \Rightarrow n = \frac{1}{3}$ .
Answer: $n^{-1} = 3$

Report a mistake

Scalar (Dot) Product question from JEE Main 2025 (23 Jan, Shift 1)

More questions on Scalar (Dot) Product