A component of a vector is

Step-by-step solution

Let a vector be represented as A = A_x i + A_y j + A_z k . The magnitude of the vector is given by A = A_x^2 + A_y^2 + A_z^2 . Since the squares of real numbers are non-negative, A_y^2 0 and A_z^2 0 . This implies that A_x^2 A_x^2 + A_y^2 + A_z^2 , which gives A_x^2 A^2 . Taking the square root on both sides, we get |A_x| A . Similarly, |A_y| A and |A_z| A . Therefore, the magnitude of any component of a vector is always less than or equal to the magnitude of the vector itself. If the vector lies entirely along a s