If a vector \(A=2 i+2 j+3 k\) and \(B=3 i+6 j+n k\) are perpendicular to each other, then the value of \(n\)…
If a vector \(A=2 i+2 j+3 k\) and \(B=3 i+6 j+n k\) are perpendicular to each other, then the value of \(n\) is
$-6$
$-0 \cdot 5$
1
$-1$
Solution
If two vectors are perpendicular, then the dot product is zero.
$\begin{aligned}
&A=2 i+2 j+3 k \\
&B=3 i+6 j+n k \\
&A \cdot B=0 \Rightarrow 6+12+3 n=0 \\
&\Rightarrow 18=-3 n \\
&\Rightarrow n=-6
\end{aligned}$
Hence the value of $n$ is $-6$.