Question

The component of a vector is

• A. always less than its magnitude
• B. always greater than its magnitude
• C. always equal to its magnitude
• D. none of these

Answer 1

The correct option is D

none of these

Components of a vector:

1. Vector components help to split a given vector into parts with respect to different directions.
2. The magnitude of the component may be less than or equal to the magnitude of the vector itself which will depend on what direction you are taking the components along.
3. The magnitude of the component may be equal to the magnitude of the vector if the projection is taken along itself, otherwise, it will always be less.
4. Consider a vector $4i$ where i is a unit vector along the x-axis.
5. In this case, the magnitude of the component of this vector along the $x$ axis is $4$, it is same as that of the vector.
6. Now, consider a vector $3i+4j$, where $i$ and $j$ are unit vectors, the magnitude of this vector is $5$ but the component's magnitude of this vector are $3$ and $4$ along the $x$ and $y$ axis respectively.
7. Hence, the component of a vector can be either less than or equal to the vector.

Thus, the correct option is option D.