If the direction cosines of a vector of magni | vedclass

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(B) The direction cosines of a vector are given as $l = \frac{2}{3}$,$m = -\frac{1}{3}$,and $n = \frac{2}{3}$.We know that a vector $\vec{V}$ with mag

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$2\hat{i}-\hat{j}+2\hat{k}$

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(B) The direction cosines of a vector are given as $l = \frac{2}{3}$,$m = -\frac{1}{3}$,and $n = \frac{2}{3}$.We know that a vector $\vec{V}$ with magnitude $|\vec{V}|$ and direction cosines $(l, m, n)$ is given by $\vec{V} = |\vec{V}|(l\hat{i} + m\hat{j} + n\hat{k})$.Given the magnitude $|\vec{V}| = 3$.Substituting the values,we get:$\vec{V} = 3 \left( \frac{2}{3}\hat{i} - \frac{1}{3}\hat{j} + \frac{2}{3}\hat{k} \right)$$\vec{V} = 2\hat{i} - \hat{j} + 2\hat{k}$.

If the direction cosines of a vector of magnitude $3$ are $\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}$,then the vector is:

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