If the two vectors A- - 2 - - 3 - - 4 k- and B- - - - 2 - - n k- are perpendicular- then the value of n is-

The correct option is D 2 Given, [ A =2 i +3 j +4 k #160;; B = i +2 j n k #160; ] They are perpendicular, [ ...

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Standard XII

Physics

Multiplication with Vectors

If the two ve...

Question

If the two vectors $\to A = 2^i + 3^j + 4^k$ and $\to B =^i + 2^j - n^k$ are perpendicular, then the value of $n$ is:-

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Solution

The correct option is D $2$
Given,
$\begin{matrix} \to A = 2 ˆ i + 3 ˆ j + 4 ˆ k \to B = ˆ i + 2 ˆ j - n ˆ k \end{matrix}$
They are perpendicular,
$\begin{matrix} \to A = 2 ˆ i + 3 ˆ j + 4 ˆ k \to B = ˆ i + 2 ˆ j - n ˆ k ∴ \to A . \to B = 0 \Rightarrow (2 ˆ i + 3 ˆ j + 4 ˆ k) . (ˆ i + 2 ˆ j - n ˆ k) = 0 \Rightarrow 2 ˆ i . ˆ i + 3 ˆ j .2 ˆ i - 4 ˆ k . n ˆ k = 0 [∵ ˆ i . ˆ j = j . ˆ k = ˆ i . ˆ k = 0] \Rightarrow 2 + 6 - 4 n = 0 [∵ ˆ i . ˆ i = ˆ j . ˆ j = ˆ k . ˆ k = 1] \Rightarrow 4 n = 8 ∴ n = 2 \end{matrix}$
Hence, Option $B$ is correct.

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If the two vectors →A=2^i+3^j+4^k and →B=^i+2^j−n^k are perpendicular, then the value of n is:-

If the two vectors $\to A = 2^i + 3^j + 4^k$ and $\to B =^i + 2^j - n^k$ are perpendicular, then the value of $n$ is:-