# Two questions involving lines and planes

I have two questions involving lines and planes. They're both fairly simple, but I'm stuck. I'm sure someone is going to point something out and it's going to make me smack my forehead.

## Homework Statement

Where does the line through*(1, 0, 1) and (4,*−2,*4) intersect the plane*x*+*y*+*z*=*10?

## The Attempt at a Solution

Okay, I know I need to get the equation of the line between (1,0,1) and (4, -2, 4). I find the direction vector to be <3, -2, 3>. Now, r(t)=r0+tv, which, using (1,0,1) as r), I find to be:

r(t)=(1-3t, 2t, 1-3t)

Once I have those, I simply plug those values into the equation of the plane to find t.

(1-3t)+(-2t)+1-3t)=10
2-8t=10
t=-1

And now I take that value of t and plug it into t(t) to get (x,y,z) coordinates. So (x,y,z)=(4, -2, 4).

However, (4, -2, 4) is incorrect.

## Homework Statement

Consider the following planes.
4x*−*3y*+*z*=*1 and*****3x*+*y*−*4z*=*4
(a) Find parametric equations for the line of intersection of the planes. (Use the parameter*t.)

## The Attempt at a Solution

So n1= <4, -3, 1> and n2=<3, 1, -4>, and I can find the direction of the line of intersection by finding the cross product of n1Xn2, which is <-13, 19, -5>. However, to find the parametric equation of the line, I still need r0, but I don't know how to find a value that is on the line.

Thanks in advance for the help.