# Homework Help: Linear Algebra Questions

1. Jun 17, 2005

### 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.

2. Jun 17, 2005

### StatusX

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

3. Jun 17, 2005

### jdstokes

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

4. Jun 18, 2005

### StatusX

so pick another one...