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

Answer: (D)

none of these

The magnitude of component of a vector (projection) may be less than or equal to the magnitude of the vector itself which will depend on what you are taking the components along. The magnitude of the component may be equal to the magnitude of the vector if and only of the projection is taken along itself, otherwise it will always be less.

For instance, consider a vector $4i$ where i is a unit vector along he x axis. Now the magnitude of the component of this vector along the x axis is 4, same as that of the vector. Now, consider a vector $3i+4j$, where $i$ and $j$ are unit vectors along x and y axis respectively, the magnitude of this vector is $5$ but the magnitude of components of this vector are $3$ and $4$ along the x and y axis respectively.