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# Find the direction cosines of the vector i + 2 j + 3k

Q.12  Find the direction cosines of the vector $\hat i + 2 \hat j + 3 \hat k$

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Let

$\vec a=\hat i + 2 \hat j + 3 \hat k$

$\left |\vec a \right |=\sqrt{1^2+2^2+3^2}=\sqrt{14}$

Hence direction cosine of $\vec a$ are

$\left ( \frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}} ,\frac{3}{\sqrt{14}}\right )$

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