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## Homework Statement

Hello!

I have one problem which seems not so difficult:

-Find the equation of line which passes throught the point M(1,0,7), parallel of the plane 3x-y+2z-15=0 and it intersects the line [tex]\frac{x-1}{4}=\frac{y-3}{2}=\frac{z}{1}[/tex]

## Homework Equations

## The Attempt at a Solution

The equation of the line will be: [tex]\frac{x-1}{a_1}=\frac{y}{a_2}=\frac{z-7}{a_3}[/tex]

So we need to find [tex]\vec{a}(a_1,a_2,a_3)[/tex] and we need three conditions in the system.

The first condition is [tex]\vec{a} \circ \vec{n}=0[/tex] or [tex](a_1,a_2,a_3)(3,-1,2)=0[/tex] or [tex]3a_1-a_2+2a_3=0[/tex].

The second condition is the intersection of two lines, and it is:

[tex]-17a_1+28a_2+12a_3=0[/tex]

What about the third condition?