Math CentralQuandaries & Queries


Question from Manis, a student: Find the ratio in which the line joining (2,4,16) and (3,5,-4)
is divided by the plane 2x-3y+z+6=0.


You can do this by finding the parametric formula of the line and then the coordinates of the point of intersection.

But it would be better to evaluate the function 2x-3y+z
at each point and see in what ratio that pair of real numbers is divided by -6. This uses the fact that linear maps preserve ratios.

Good Hunting!

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