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Direction Cosines

Find the comp...

Question

Find the components of a unit vector which is perpendicular to the vectors $^i + 2^j -^k$ and $3^i -^j + 2^k$ .

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Solution

Vector perpendicular to $1^i + 2 j - 1 k$ and $3 i - j + 2 k$ is $∣ ∣ ∣ ∣ \begin{matrix} i & j & k 1 & 2 & - 1 3 & - 1 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$\Rightarrow 3 i - 5 j - 7^k$
$\Rightarrow$ Unit vector of this vector
$\Rightarrow \frac{3 i - 5 j - 7 k}{\sqrt{9 + 25 + 49}}$
$= \frac{3 i - 5 j - 7 k}{\sqrt{83}}$ .

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