Question

What are the coordinates of the shadow cast on the xy plane by a small object placed at the point (10,7,20) assuming that the sun's rays are parallel to the vector (5,3,-2)?

Answer 1

We are given with two coordinates
(10, 7, 20) and
(5, 3, -2)
Which can be used to create a linear equation represented by vectors
<x, y, z> = <x0, y0, z0> + t<mx, my, mz>
We can get the slope by
<mx, my, mz> = <10, 7, 20> - <5, 3, -2> = <5, 4, 22>

<x, y, z> = <x0, y0, z0> + t<5, 4, 22>
At z = 0, and using the coordinates of either of the two points, the coordinates o the shadow of the point can be determined.