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(B) The direction cosines of a vector $\vec{a} = x \hat{i} + y \hat{j} + z \hat{k}$ are given by $\frac{x}{|\vec{a}|}, \frac{y}{|\vec{a}|}, \frac{z}{|

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$\frac{-2}{\sqrt{30}}, \frac{1}{\sqrt{30}}, \frac{-5}{\sqrt{30}}$

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(B) The direction cosines of a vector $\vec{a} = x \hat{i} + y \hat{j} + z \hat{k}$ are given by $\frac{x}{|\vec{a}|}, \frac{y}{|\vec{a}|}, \frac{z}{|\vec{a}|}$.Given $\vec{a} = -2 \hat{i} + \hat{j} - 5 \hat{k}$.First,calculate the magnitude of the vector: $|\vec{a}| = \sqrt{(-2)^2 + (1)^2 + (-5)^2} = \sqrt{4 + 1 + 25} = \sqrt{30}$.The direction cosines are $\frac{-2}{\sqrt{30}}, \frac{1}{\sqrt{30}}, \frac{-5}{\sqrt{30}}$.Thus,option $B$ is correct.

The direction cosines of the vector $\vec{a} = -2 \hat{i} + \hat{j} - 5 \hat{k}$ are

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