Find a vector in the direction of vector 5 ha | vedclass

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Question

(A) Let $\vec{a} = 5\hat{i} - \hat{j} + 2\hat{k}$.The magnitude of $\vec{a}$ is $|\vec{a}| = \sqrt{5^2 + (-1)^2 + 2^2} = \sqrt{25 + 1 + 4} = \sqrt{30}

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 $\vec{a} = 5\hat{i} - \hat{j} + 2\hat{k}$.The magnitude of $\vec{a}$ is $|\vec{a}| = \sqrt{5^2 + (-1)^2 + 2^2} = \sqrt{25 + 1 + 4} = \sqrt{30}$.The unit vector in the direction of $\vec{a}$ is $\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{5\hat{i} - \hat{j} + 2\hat{k}}{\sqrt{30}}$.$A$ vector of magnitude $8$ units in the direction of $\vec{a}$ is $8\hat{a} = 8 \left( \frac{5\hat{i} - \hat{j} + 2\hat{k}}{\sqrt{30}} \right)$.Thus,the required vector is $\frac{40}{\sqrt{30}}\hat{i} - \frac{8}{\sqrt{30}}\hat{j} + \frac{16}{\sqrt{30}}\hat{k}$.

Find a vector in the direction of vector $5 \hat{i}-\hat{j}+2 \hat{k}$ which has magnitude $8$ units.

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