Point at which line and plane intersect

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kanai
kanai 2013-10-26
Hi
If I have a line say
x=2t-1 y=4t+2 z=1-3t
and a Plane 2x-3y+3z-13=0
How do I find the point intersection in the form (x,y,z). I am aware this is a very simple scenario and the principle is just to substitute the x y and z values into the plane equation, work out t and then resubstitute t back into the parametric line.
However I have many calculations to do and most numbers are to 5 decimal points. Would appreciate the help from the community.

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