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…

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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 _____.

Aicharya · Accepted Answer

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

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

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