JEE Main 2025 Jan 23 Shift 1, Physics Q22: Units And Measurement

JEE Main2025Jan 23, Shift 1Physics

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

Your answer

Solution

Two conditions: equal magnitudes and perpendicularity.

Equal magnitudes: $∣ A ∣^{2} = ∣ B ∣^{2} \Rightarrow 4 + 9 n^{2} + 4 = 4 + 4 + 16 p^{2} \Rightarrow 9 n^{2} = 16 p^{2} \Rightarrow p = \pm \frac{3 n}{4}$ .

Perpendicularity: $A \cdot B = 0 \Rightarrow 4 - 6 n + 8 p = 0$ .

Substituting $p = + \frac{3 n}{4}$ : $4 - 6 n + 6 n = 4 \neq = 0$ (rejected).

Substituting $p = - \frac{3 n}{4}$ : $4 - 6 n - 6 n = 0 \Rightarrow 12 n = 4 \Rightarrow n = \frac{1}{3}$ .

$∴ n^{- 1} = 3$ .

Practice more Physics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →