If A→=3i^+4j^ and B→=7i^+24j^ , the vector having the same magnitude as B→ and parallel to A→ is :

C→=BA^=72+242(3i^+4j^)32+42=25×(3i^+4j^)5 =15i^+20j^

C→=BA^=72+242(3i^+4j^)32+42=25×(3i^+4j^)5 =15i^+20j^

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

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_{$5 \hat{i} + 20 \hat{j}$}

_{$15 \hat{i} + 10 \hat{j}$}

_{$20 \hat{i} + 15 \hat{j}$}

_{$15 \hat{i} + 20 \hat{j}$}

answer is D.

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$\vec{C} = B \hat{A} = \sqrt{7^{2} + 24^{2}} \frac{(3 \hat{i} + 4 \hat{j})}{\sqrt{3^{2} + 4^{2}}} = 25 \times \frac{(3 \hat{i} + 4 \hat{j})}{5}$

$= 15 \hat{i} + 20 \hat{j}$

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