How do you find the range of the scalar triple product of the vectors <cos alpha, cos beta, 0>, <0, cos beta, cos gamma> and <cos alpha, 0, cos gamma>?
1 Answer
Explanation:
The triple scalar product of vectors
We will use that to calculate the given scalar triple product.
Let
Then we have:
=det((cos(alpha),cos(beta),0),(0,cos(beta),cos(gamma)),(cos(alpha),0,cos(gamma)))
=cos(alpha)(cos(beta)cos(gamma)-0cos(gamma))
-cos(beta)(0cos(gamma)-cos(alpha)cos(gamma))
+0(0*0-cos(alpha)cos(beta))
=2cos(alpha)cos(beta)cos(gamma)
Thus, it suffices to find the range of
With no restrictions on
Thus their product will also have the range
Multiplying by
Thus the range of the scalar triple product of