If A = 3hat i + 4hat j and B = 7hat i + 24hat | vedclass

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(D) First,calculate the magnitude of vector $B$: $|B| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$. Next,find the unit vector in the direc

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$15\hat i + 20\hat j$

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(D) First,calculate the magnitude of vector $B$: $|B| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$. Next,find the unit vector in the direction of $A$: $|A| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5$. $\hat A = \frac{A}{|A|} = \frac{3\hat i + 4\hat j}{5}$. The required vector has the same magnitude as $B$ $(25)$ and is parallel to $A$ (in the direction of $\hat A$): $	ext{Required Vector} = |B| \cdot \hat A = 25 \cdot \left( \frac{3\hat i + 4\hat j}{5} ight) = 5(3\hat i + 4\hat j) = 15\hat i + 20\hat j$.

If $A = 3\hat i + 4\hat j$ and $B = 7\hat i + 24\hat j,$ the vector having the same magnitude as $B$ and parallel to $A$ is

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