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Solve the following.
If the two vectors 3î + aĵ + k̂ and 2î - ĵ + 8k̂ are perpendicular to each other, then find the…
If the two vectors $3\hat{i} + a\hat{j} + \hat{k}$ and $2\hat{i} - \hat{j} + 8\hat{k}$ are perpendicular to each other, then find the value of $a$.
Answer
Answer
Perpendicular vectors have zero dot product.
$(3)(2) + (a)(-1) + (1)(8) = 0 \Rightarrow 14 - a = 0$
Hence $a = 14$.
Final answer: 14