First off... not my homework. it's the wifes! She's in landscape architecture and is having trouble understanding a question that was given with little explaination. In fact the instructor of the course couldn't remember how to do it and so they had no explanation.
The question is:
Given a point, q, on a plane,p, as well as a slope,s, along a vector,v, which lies on the projection of P onto the xy plane, find 3 other points.
p0------p1(i have height at p1) | | p0__x__p1 | | | / | | y | /v p2------p3 | /
so we started out by extending v, from p1, until it intersected the line from po->p2. since the points fall on a regular grid, we knew |x| = |p0-p1| = 50m, and used the magnitude of V when x = 50 to get y = 22.19m. the projection of V onto XY was measured at 55m. Since we have slope along V, a bit of pythagoras gave us dz of 4.565m. so now I have a vector,q<50,22.19,4.565> that lies along the plane,p, and the height at p1. How can i calculate the x and y components of the slope(gradient?), so that i can find p0.z = p1.z + xm, p3.z = p1.z+yn, and p2.z = p1.z+xm+yn.