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

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Aicharya · Accepted Answer

The direction cosines of vector $\mathbf{a}=-2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-5 \hat{\mathbf{k}}$ are $-\frac{2}{|\mathbf{a}|}, \frac{1}{|\mathbf{a}|}, \frac{-5}{|\mathbf{a}|}$ $\because \quad|\mathbf{a}|=\sqrt{4+1+25}=\sqrt{30}$ $\therefore$ Required direction cosines are $-\frac{2}{\sqrt{30}}, \frac{1}{\sqrt{30}},-\frac{5}{\sqrt{30}}$ Hence, option (b) is correct.

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

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