Question

The magnitude of a component of a vector must be(a) less than or equal to the magnitude of the vector.(b) equal to the magnitude of the vector.(c) greater than or equal to the magnitude of the vector.(d) less than, equal to, or greater than the magnitude of the vector.

Short answer

The magnitude of a component of a vector must be less than or equal to the magnitude of the vector.

Step-by-step solution

Step 1. Magnitude of a component of a vector

When the velocities of objects are along a similar line, then, in order to obtain the relative velocity, simple addition and subtraction are enough.

The components make up the two sides of a right triangle in a vector if the vector is the hypotenuse. Also, the legs of that triangle should not be greater than the hypotenuse. So, options (c) and (d) are incorrect answers.

Step 2. Vector addition

Similarly, option (b) is incorrect because the magnitude of a component will be equal to the magnitude of the vector only if the vector is parallel to the component. In all other cases, the component’s magnitude is always less than the magnitude of the vector.

Thus, option (a) is the correct answer.