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Question

Find the coordinates of the point where line through the points A=(3,4,1) and B=(5,1,6) crosses the xy-plane.

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Solution

A=(3,4,1);B=(5,1,6)
The line can be written as r=(3,4,1)+t(2,3,5)
This also can be written as t=x32=y43=z15
Since we need the coordinates of the point where the line crosses the x-y plane, we make z equal to zero.
t=015=15
x32=15
5x15=2 or x=135
Similarly, y43=15
5y20=3 or y=235
The coordinates thus become (135,235,0)

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