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

The Correct Option is C

$ \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}. $