Which of the following statements is true?
a. the components of a vector must be nonzero.
b. a vector’s magnitude is equal to the sum of the squares of its components.
c. the magnitude of a vector is never negative.
d. the direction of a vector is always less than the magnitude.

C. The magnitude of a vector is never negative.

Step-by-step explanation:

The components of a vector are their corresponding measurements on each axis. In the plane, these axes are x and y, so a vector on a plane has a component for x and a component for y.

Thus, the magnitude of said vector can be found by the Pythagorean theorem.

R being the magnitude of the vector:

I attached an image so you can see where this comes from.

We can see in the equation that we have two squared quantities, this will always be a positive number, an the root squeare of a positive number is also positive. So the magnitude will never be negative

We discard the other options because:

A: the components of a vector can be nonzero, it is called the zero vector.

B. As we found, the value for the magnitud is the square root of the sum of the squares of its components.

D. The direction can be an angle, or a cardinal direction like north or south, so we can't compare this directly with a magnitud that is just a number.

answer4 to the second power is 16

and 4 to the third power is 64,