Hi, we are told that Y is a plane in R3 and contains the Point P(-1,3,7) and a line given by the equation (x-1)/2 = (y+1)/2 = z/3.
How would we use this information to work out the cartesian equation of the plane Y?
You can use the following ideas:
1)Any plane in $\displaystyle \mathbb{R}^3$ is of the form $\displaystyle ax+by+cz+d = 0$ and the point P satisfies it.
2) For $\displaystyle t \in \mathbb{R}, x = 2t+1, y = 2t - 1, z = 3t$. Why is this true?
Can you solve for a,b,c,d?