# Linear Algebra Questions

#### jdstokes

Let $\ell$ be the line given by $\frac{x-1}{2}=\frac{y+2}{-3}=\frac{z-3}{4}$. Write down a system of two equations in the three unknowns $a$, $b$, $c$ whose solutions give all planes $ax + by + cz = 1$ in which $\ell$ lies, and solve the system. I can certainly write that $a -2b + 3c = 1$. I can't figure out how to obtain the second equation.

Thanks

James.

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#### StatusX

Homework Helper
Just pick two points on the line and plug in for (x,y,z).

#### jdstokes

I picked (1,-2,3) and I only have one equation $a -2b + 3c = 1$.

#### StatusX

Homework Helper
so pick another one...

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