Consider the curve r(t) = (a cos t + b sin t)i + (c cos t +

Question:

Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t + f sin t)k, where a, b, c, d, e, and f are real numbers. It can be shown that this curve lies in a plane.

Assuming the curve lies in a plane, show that it is a circle centered at the origin with radius R provided a² + c² + e² = b² + d² + f² = R² and ab + cd + ef = 0.