A vector which is in the direction of (3, 6, | vedclass

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(C) Let the given vector be $\vec{a} = 3\hat{i} + 6\hat{j} + 2\hat{k}$.First,find the magnitude of $\vec{a}$:$|\vec{a}| = \sqrt{3^2 + 6^2 + 2^2} = \sq

Vedclass · Accepted Answer

$\left(\frac{12}{7}, \frac{24}{7}, \frac{8}{7}\right)$

Vedclass · Answer

(C) Let the given vector be $\vec{a} = 3\hat{i} + 6\hat{j} + 2\hat{k}$.First,find the magnitude of $\vec{a}$:$|\vec{a}| = \sqrt{3^2 + 6^2 + 2^2} = \sqrt{9 + 36 + 4} = \sqrt{49} = 7$.Now,find the unit vector in the direction of $\vec{a}$:$\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{3}{7}\hat{i} + \frac{6}{7}\hat{j} + \frac{2}{7}\hat{k}$.$A$ vector with magnitude $4$ in the direction of $\vec{a}$ is given by $4 	imes \hat{a}$:$4 	imes \left(\frac{3}{7}\hat{i} + \frac{6}{7}\hat{j} + \frac{2}{7}\hat{k}ight) = \left(\frac{12}{7}, \frac{24}{7}, \frac{8}{7}ight)$.

$A$ vector which is in the direction of $(3, 6, 2)$ and has magnitude $4$ is $.......$

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