What is used to compute the magnitude of a vector?

The magnitude of a vector is computed using the formula that involves the square root of the sum of the squares of its components. Specifically, for a three-dimensional vector with components x, y, and z, the correct formula to find the magnitude is the square root of the sum of the squares of each component: ( \sqrt{x^2 + y^2 + z^2} ). This calculation reflects the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the length of the vector) is equal to the sum of the squares of the other two sides.

For example, in a three-dimensional space, if you think of the components x, y, and z as the respective distances along the three axes, the magnitude gives you the straight-line distance from the origin to the point represented by the vector in that space. This relationship is foundational in physics and engineering, especially in dealing with forces, velocities, and other vector quantities.

Other choices do not represent the correct method for finding a vector's magnitude. The sum of the components, the average of the components, or the square root of their sum do not yield the geometric distance that the magnitude represents. Therefore, the essence