point of intersection between a line and a plane

[mathstresser]

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?

 

[pka]

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.

 

[galactus]

\(\displaystyle (1+t)-(-1+3t)+4(2+4t)=7\)

\(\displaystyle 14t+10=7\)

 

[mathstresser]

Thank you!