overrightarrow{A} = 4hat{i} + 3hat{j} and ove | vedclass

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Question

(A) First, find the magnitude of vector $\overrightarrow{B}$:$|\overrightarrow{B}| = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20}$.Next, find the unit

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$\sqrt{20}(4\hat{i} + 3\hat{j})$

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(A) First, find the magnitude of vector $\overrightarrow{B}$:$|\overrightarrow{B}| = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20}$.Next, find the unit vector in the direction of $\overrightarrow{A}$:$|\overrightarrow{A}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = 5$.$\hat{A} = \frac{\overrightarrow{A}}{|\overrightarrow{A}|} = \frac{4\hat{i} + 3\hat{j}}{5}$.The required vector $\overrightarrow{R}$ is parallel to $\overrightarrow{A}$ and has magnitude $5|\overrightarrow{B}| = 5\sqrt{20}$.Thus, $\overrightarrow{R} = (5|\overrightarrow{B}|) \hat{A} = (5\sqrt{20}) \left( \frac{4\hat{i} + 3\hat{j}}{5} \right) = \sqrt{20}(4\hat{i} + 3\hat{j})$.

$\overrightarrow{A} = 4\hat{i} + 3\hat{j}$ and $\overrightarrow{B} = 4\hat{i} + 2\hat{j}$. Find a vector parallel to $\overrightarrow{A}$ but with a magnitude five times that of $\overrightarrow{B}$.

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