Two particles are located at equal distance from origin. The position vectors of those are represented by A→=2i^+3nj^+2k^ and B→=2i^-2j^+4pk^, respectively. If both the vectors are at right angle to each other, the value of n–1 is____.

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

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

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answer is 3.

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Detailed Solution

$\begin{array}{l} \vec{A} \cdot \vec{B} = 0 \\ 4 - 6 n + 8 p = 0 \\ | \vec{A} | = | \vec{B} | \\ 4 + 9 n^{2} + 4 = 4 + 4 + 16 p^{2} \\ 9 n^{2} = 16 p^{2} \end{array}$
$\begin{array}{l} P = + \frac{3}{4} n \\ 4 - 6 n \pm 6 n = 0 \\ 12 n = 4 \\ n = \frac{1}{3} \end{array}$