a. Write the equation of the line of intersection of the two planes 4x+2y-z=8 and x+2y-z=2 , then b) Find the?

Question

equation of the plane that passes through the point (1, 2, 3) and is perpendicular to the line of intersection you found in part a.

Answer 1

(a)
4x + 2y - z = 8
x + 2y - z = 2

Subtracting the second equation from the first we have:
3x = 6
x = 2

x + 2y - z = 2
2 + 2y - z = 2
2y - z = 0
2y = z

Pick a point on the line. Select (2,0,0).
The equation of the line of intersection is:

L1 = <2,0,0> + t<0,1,2>
__________________________

(b)
The normal vector for the plane perpendicular to the line of intersection is the directional vector for the line. So the equation of the plane is:

0(x - 1) + 1(y - 2) + 2(z - 3) = 0
y - 2 + 2z - 6 = 0
y + 2z - 8 = 0

Answer 2

I was going to say the same thing..

its one thing to ask for help on a homework problem but its another not to copy down the problem and expect someone to answer it for you!

If you have a homework problem like this, my guess is your math level is high enough that you can figure it out yourself with little difficulty. Its not that hard!

Answer 3

Math was invented by a man who could not conquer a third world nation and tourture people directly.

Answer 4

4x+2y-z=8
-)x+2y-z=2
-----------------------
3x=6
x=2

replace x=2 in the first expression
2y-z=0

Answer: x=2, 2y-z=0

Answer 5

do your own homework