point of intersection between a line and a plane

mathstresser

Junior Member
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Jan 28, 2006
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134
Find the point of intersection between the line <x,y,z>=<1,-1,2>+<1,3,4>t and the plane x-y+4z=7.

What do I do?
 
The parametric equation of the line is
\(\displaystyle \L
\left\{ \begin{array}{l}
x & = & 1 + t \\
y & = & - 1 + 3t \\
z & = & 2 + 4t \\
\end{array} \right.\)
Subsitute into the plane solve for t.
 
\(\displaystyle (1+t)-(-1+3t)+4(2+4t)=7\)

\(\displaystyle 14t+10=7\)
 
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