Find a vector in the direction of vector vec{ | vedclass

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(A) The magnitude of the vector $\vec{a} = \hat{i} - 2\hat{j}$ is $|\vec{a}| = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5}$.The unit vector in the d

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$\frac{7}{\sqrt{5}} \hat{i} - \frac{14}{\sqrt{5}} \hat{j}$

Vedclass · Answer

(A) The magnitude of the vector $\vec{a} = \hat{i} - 2\hat{j}$ is $|\vec{a}| = \sqrt{1^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5}$.The unit vector in the direction of $\vec{a}$ is given by $\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{1}{\sqrt{5}}(\hat{i} - 2\hat{j}) = \frac{1}{\sqrt{5}}\hat{i} - \frac{2}{\sqrt{5}}\hat{j}$.$A$ vector of magnitude $7$ in the direction of $\vec{a}$ is $7\hat{a} = 7 \left( \frac{1}{\sqrt{5}}\hat{i} - \frac{2}{\sqrt{5}}\hat{j} \right) = \frac{7}{\sqrt{5}}\hat{i} - \frac{14}{\sqrt{5}}\hat{j}$.

Find a vector in the direction of vector $\vec{a} = \hat{i} - 2\hat{j}$ that has magnitude $7$ units.

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