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} $
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} $
Updated On: Mar 18, 2026
- $ {{A}^{\to }} $ and $ {{B}^{\to }} $
- $ {{A}^{\to }} $ and $ {{C}^{\to }} $
- $ {{A}^{\to }} $ and $ {{D}^{\to }} $
- $ {{C}^{\to }} $ and $ {{D}^{\to }} $
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The Correct Option is C
Solution and Explanation
$ \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}. $
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Concepts Used:
Vector Basics
What is a Vector Quantity?
Vector Quantity is a physical quantity that is specified not only by its magnitude but also by its direction. A vector quantity whose magnitude is equal to one and has direction is called a unit vector.
Examples of vector quantity are-
- Displacement
- Linear momentum
- Momentum
- Acceleration
- Force
- Electric field
- Angular velocity
- Polarization