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Question
If the vectors \[3 \hat{i} + m \hat{j} + \hat{k} \text{ and } 2 \hat{i} - \hat{j} - 8 \hat{k}\] are orthogonal, find m.
Solution
\[\text{ It is given that the vectors are othgonal. So, their dot product is zero }.\]
\[\left( 3 \hat{i} + m \hat{j} + \hat{k} \right) . \left( 2 \hat{i} - \hat{j} - 8 \hat{k} \right) = 0\]
\[ \Rightarrow 6 - m - 8 = 0\]
\[ \Rightarrow - m - 2 = 0\]
\[ \Rightarrow m = - 2\]
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