Please Help!

Find the point P where the line x=1+t y=2t z=-3t intersects the plane x+y-z=-2

Find the distance from the point (-1,2,3) to the plane -1x+0y-2z=5

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- Jun 9th 2008, 06:10 PMkarnold9find the distance, find the point
Please Help!

Find the point P where the line x=1+t y=2t z=-3t intersects the plane x+y-z=-2

Find the distance from the point (-1,2,3) to the plane -1x+0y-2z=5 - Jun 9th 2008, 06:19 PMTheEmptySet
plug x,y,z into the equation of the plane to get

$\displaystyle (1+t)+(2t)-(-3t)=-2 \iff 6t+1=-2 \iff t=-\frac{1}{2}$

Plug this value into the parametric equation to find the point.

for part b write the plane is this form

$\displaystyle ax+by+cz+d=0$ and use the formula from this link

Point-Plane Distance -- from Wolfram MathWorld

I hope this helps.