Question

Of the vectors given below, the parallel vectors are, ${{A}^{\to }}=6\widehat{i}+8\widehat{j}$ ${{B}^{\to }}=210\widehat{i}+280\widehat{k}$ ${{C}^{\to }}=5.1\widehat{i}+6.8\widehat{k}$ ${{D}^{\to }}=3.6\widehat{i}+6\widehat{j}+48\widehat{k}$

• A. ${{A}^{\to }}$ and ${{B}^{\to }}$
• B. ${{A}^{\to }}$ and ${{C}^{\to }}$
• C. ${{A}^{\to }}$ and ${{D}^{\to }}$
• D. ${{C}^{\to }}$ and ${{D}^{\to }}$

Answer 1

Answer: (C)

${{A}^{\to }}$ and ${{D}^{\to }}$

Answer 2

$\vec{A}=6\hat{i}+8\hat{j}$ $\vec{B}=210\hat{i}+280\hat{k}$ $\vec{C}=5.1\hat{i}+6.8\hat{j}=\frac{1}{20}(6\hat{i}+8\hat{j})$ $\vec{D}=3.6\hat{i}+8\hat{j}+4.8\hat{k}$ Hence, it is clear that \text{\vec{A}} and $\vec{C}$ are parallel and we can write as $\vec{A}=\frac{1}{20}\vec{C}$ This implies that \text{\vec{A}} is parallel to $\vec{C}$ and magnitude of \text{\vec{A}} is $\frac{1}{20}.$