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## Homework Statement

Consider the line and plane below.

x = 5-5t, y = 3+7t, z = 10t

ax + by + cz = d

Find values of a, b, c, and d so that the plane is perpendicular to the line and through the point (2, 1, 2).

## Homework Equations

F

_{grad}=(x',y',z') is perp to surface

if [tex]\vec{v}[/tex]

_{1}[tex]\bullet[/tex][tex]\vec{v}[/tex]

_{2}=0

then v

_{1}[tex]\bot[/tex]v

_{2}

## The Attempt at a Solution

when I put those x,y,z values together I get a parametric equation that equals <5,3,0>+t<-5,7,10>

the starting point <5,3,0> I think is not relevant to finding a perpendicular vector,

I just need to find a vector perpendicular to t<-5,7,10> that goes through (2,1,2) i think? but i'm not sure how to do this..

then once I find the vector thats perp to t<-5,7,10>(dot)<a,b,c>=0

once I know a,b,c I can solve for d