(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find an equation of the plane that passes through the point (6,0,-2) and contains the line x=4-2t, y=3+5t, z=7+4t.

2. Relevant equations

3. The attempt at a solution

Here's what I did:

I substituted t=2 to get:

x=0, y=17, z= 15

So in total, we have three points that the plane contains: P1(6,0,-2), P2(4,3,7), P3(0,17,15)

Vector P1P2=<-2,3,9>

Vector P1P3=<-6,17,17>

I took a cross product of these vectors to get <-102,-20,-16>

I used the point P1(6,0,-2) to obtain:

-102(x-6)-20(y-0)-16(z+2)=0

But the solution is 33(x-6)-10(y-0)-4(z+2)=0

I'm unable to understand what I did wrong. I'd really appreciate any help!

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# Homework Help: Finding the equation of a plane

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