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

Correct answer: 0 aligned & A · B =0 & 4-6 n+8 p=0 & | ~A |=| B | & 4+9 n^2+4=4+4+16 p^2 & 9 n^2=16 p^2 & P=+(3)/(4) n & 4-6 n ± 6 n=0 & 12 n=4 & n=(1)/(3) aligned

JEE Main 202523 JanuaryMorning Shift

Exam: JEE Main
Year: 2025
Date: 23 January
Shift: Morning Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2025 · 23 January · Morning Shift · Physics · Mathematics in Physics

Two particles are located at equal distance from origin. The...

Two particles are located at equal distance from origin. The position vectors of those are represented by

\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k}

and

\bar{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

\mathrm{n}^{-1}

is _____ .

Correct answer

Step-by-step solution

\begin{aligned} & \overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}=0 \\ & 4-6 \mathrm{n}+8 \mathrm{p}=0 \\ & |\overrightarrow{\mathrm{~A}}|=|\overrightarrow{\mathrm{B}}| \\ & 4+9 \mathrm{n}^2+4=4+4+16 \mathrm{p}^2 \\ & 9 \mathrm{n}^2=16 \mathrm{p}^2 \\ & \mathrm{P}=+\frac{3}{4} \mathrm{n} \\ & 4-6 \mathrm{n} \pm 6 \mathrm{n}=0 \\ & 12 \mathrm{n}=4 \\ & \mathrm{n}=\frac{1}{3}\end{aligned}

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