The vector in the direction of vector 5 hat{i | vedclass

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Question

(A) Let the given vector be $\vec{a} = 5 \hat{i} - \hat{j} + 2 \hat{k}$.First,find the magnitude of vector $\vec{a}$:$|\vec{a}| = \sqrt{5^2 + (-1)^2 +

Vedclass · Accepted Answer

$\frac{40}{\sqrt{30}} \hat{i} - \frac{8}{\sqrt{30}} \hat{j} + \frac{16}{\sqrt{30}} \hat{k}$

Vedclass · Answer

(A) Let the given vector be $\vec{a} = 5 \hat{i} - \hat{j} + 2 \hat{k}$.First,find the magnitude of vector $\vec{a}$:$|\vec{a}| = \sqrt{5^2 + (-1)^2 + 2^2} = \sqrt{25 + 1 + 4} = \sqrt{30}$.The unit vector in the direction of $\vec{a}$ is given by $\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{5 \hat{i} - \hat{j} + 2 \hat{k}}{\sqrt{30}}$.$A$ vector of magnitude $8$ units in the direction of $\vec{a}$ is $8 \hat{a} = 8 	imes \left( \frac{5 \hat{i} - \hat{j} + 2 \hat{k}}{\sqrt{30}} ight) = \frac{40}{\sqrt{30}} \hat{i} - \frac{8}{\sqrt{30}} \hat{j} + \frac{16}{\sqrt{30}} \hat{k}$.Thus,the correct option is $A$.

The vector in the direction of vector $5 \hat{i} - \hat{j} + 2 \hat{k}$ with a magnitude of $8$ units is:

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