Question

Why the magnitude of the rectangular component of a vector can’t be greater than the magnitude of the vector itself?

Answer 1

The magnitude of rectangular component of a vector itself cannot be greater them the magnitude of vector itself because the rectangular component of a vector A and A_x = A cos θ and A_y = A sin θ. As sin θ and cos θ both are ≤ 1, s both A_X and A_y cannot be greater than A.