Question

If $ \vec{a} = 4\hat {i} + 6\hat {j} $ and $\vec {b} = 3\hat{j} + 4\hat{k} $ , then the vector form of component of $ a $ along $ b $ is

• A. $ \frac{18}{10\sqrt{3}}\left(3\hat{j}+4\hat{k}\right) $
• B. $ \frac {18}{25} \left(3\hat{j}+4\hat{k}\right) $
• C. $ \frac{18}{\sqrt{3}}\left(3\hat{j}+4\hat{k}\right) $
• D. $ \frac {18}{25} \left(4\hat{i}+6\hat{j}\right) $

Answer 1

Answer: (B)

The component of $a$ along $b$
$=\left(\frac{ b \cdot a }{| b |^{2}}\right) b=\frac{(3 \hat{\jmath}+4 \hat{ k }) \cdot(4 \hat{\imath}+6 \hat{\jmath})}{|5|^{2}}(3 \hat{\jmath}+4 \hat{ k })$
$=\frac{18}{25}(3 \hat{\jmath}+4 \hat{ k })$