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 ______ .

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Equal distances: $4+9n^2+4=4+4+16p^2\Rightarrow3n=\pm4p$. Perpendicular: $\vec A\cdot\vec B=4-6n+8p=0$. With $p=\frac{3n}4$ this gives $4=0$ (impossible), so $p=-\frac{3n}4$: $4-6n-6n=0$, $n=\frac13$ and $n^{-1}=3$. Answer: 3.

Q. 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 ______ .

Explanation

Reviewed by Dr. Abubacker

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