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## Homework Statement

Hello!

Find the equation of the projection of the line [tex]\frac{x}{4}=\frac{y-4}{3}=\frac{z+1}{-2}[/tex] of the plane x-y+3z+8=0.

So the line projects itself on the plane...

## Homework Equations

## The Attempt at a Solution

First I find equation of line which passes throught the line and it has vector "a" parallel to the normal vector of the plane...

The equation of that line is: [tex]\frac{x}{1}=\frac{y-4}{-1}=\frac{z+1}{3}[/tex]

The equation of the line we need to find is probably: [tex]\frac{x-x_1}{4}=\frac{y-y_1}{3}=\frac{z-z_1}{-2}[/tex]

So we just need to find the point...

That point is [tex]M(\frac{1}{11},4-\frac{1}{11},-1+3\frac{1}{11})[/tex]

But in my textbook results I get tottaly different solution: [tex]\frac{x+9}{7}=\frac{y+1}{4}=\frac{z}{-1}[/tex]

I don't know what is the problem. Please help.

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