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## Homework Statement

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

## Homework Equations

## 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.)

## Homework Equations

## 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.