The direction cosines of the vector 3hat{i} - | vedclass

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(B) Let the vector be $\vec{A} = 3\hat{i} - 4\hat{j} + 5\hat{k}$.The magnitude of the vector is $|\vec{A}| = \sqrt{3^2 + (-4)^2 + 5^2} = \sqrt{9 + 16

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$\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{1}{\sqrt{2}}$

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(B) Let the vector be $\vec{A} = 3\hat{i} - 4\hat{j} + 5\hat{k}$.The magnitude of the vector is $|\vec{A}| = \sqrt{3^2 + (-4)^2 + 5^2} = \sqrt{9 + 16 + 25} = \sqrt{50} = 5\sqrt{2}$.The direction cosines $(l, m, n)$ are given by $\frac{x}{|\vec{A}|}, \frac{y}{|\vec{A}|}, \frac{z}{|\vec{A}|}$.Thus,the direction cosines are $\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{5}{5\sqrt{2}}$.Simplifying the third term,$\frac{5}{5\sqrt{2}} = \frac{1}{\sqrt{2}}$.Therefore,the direction cosines are $\frac{3}{5\sqrt{2}}, \frac{-4}{5\sqrt{2}}, \frac{1}{\sqrt{2}}$.

The direction cosines of the vector $3\hat{i} - 4\hat{j} + 5\hat{k}$ are

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