Question: Consider the curve r(t) = (a cos t + b sin t)i + (c cos t + d sin t)j + (e cos t +
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.
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