Mathematics in Physics

JEE Main level, numerical answer, medium

4 of 121

Question 4 of 121

Two particles are located at equal distance from origin. The position vectors of those are represented by Aˉ=2i^+3nj^+2k^\bar{A}=2 \hat{i}+3 n \hat{j}+2 \hat{k} and Bˉ=2i^−2j^+4pk^\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 n−1\mathrm{n}^{-1} is _____ .

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Answer: 3

A→⋅B→=04−6n+8p=0∣ A→∣=∣B→∣4+9n2+4=4+4+16p29n2=16p2P=+34n4−6n±6n=012n=4n=13\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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