The direction cosines of the vector hat{i}-2h | vedclass

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(C) Let the vector be $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$.First,we find the magnitude of the vector $\vec{a}$:$|\vec{a}| = \sqrt{(1)^2 + (-2)^2

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$\frac{1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$

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(C) Let the vector be $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k}$.First,we find the magnitude of the vector $\vec{a}$:$|\vec{a}| = \sqrt{(1)^2 + (-2)^2 + (3)^2} = \sqrt{1 + 4 + 9} = \sqrt{14}$.The direction cosines $(l, m, n)$ of a vector $x\hat{i} + y\hat{j} + z\hat{k}$ are given by $\frac{x}{|\vec{a}|}, \frac{y}{|\vec{a}|}, \frac{z}{|\vec{a}|}$.Substituting the values,we get:$l = \frac{1}{\sqrt{14}}$,$m = \frac{-2}{\sqrt{14}}$,$n = \frac{3}{\sqrt{14}}$.Thus,the direction cosines are $\frac{1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$.

The direction cosines of the vector $\hat{i}-2\hat{j}+3\hat{k}$ are . . . . . . .

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