I am having a bit of trouble-Most of the working out has been done .My problem is in green text.Thanks.
Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (2,0,0),(0,2,0),(0,0,3).
first z was integrated first in this question
but what I dont understand is what is meant by "shadow" ..Please see below.
we know that the equation of the plane is :
6x-12+6y+4z Here is a diagram:insert pic.
the normal found was 6i+6j+4k
now after the z limits were found the y limits were found .
The solutions I have state that where z=0 a line parallel to the y axis will enter the "shadow" at y=0 and exits throu point on line passing thru the two points (2,0) and (0,2),then equation of this line is y=-x+2.