Question

Given planes -9x + 4y + 8z = 14 and 4x -5y + 6z = 8. Let P(x0, y0, z0) be a point on the line of intersection of the planes and suppose that x0 = 12. Find y0 and z0

Answer 1

we are given 2 vectors to work with, and thats about it right

Answer 2

go ahead and let x0 be 12 in the plane equations to get these into line formats

Answer 3

-9(12) + 4y + 8z = 14

-108 +4y +8z = 14

4y = -8z - 94

y = -2z - 94/4


4(12) -5y + 6z = 8

48 -5y +6z = 8

-5y = -6z -40

y = 6/5 z +8

right?

Answer 4

you gotta let me know when i forget how to add :) lets try that again

Answer 5

-9(12) + 4y + 8z = 14

-108 +4y +8z = 14

4y = -8z +122

y = -2z + 122/4

Answer 6

i see that can be reduced more

y = -z + 61/2

Answer 7

the rest looks good;

y = 6/5 z +8
y = -z + 61/2

now the we have reduced them to lines; we can find where they cross by completing the system of equations we have developed

Answer 8

do you agree? or is there another method you had in mind that you needed help on?

Answer 9

ops sorry, was working another problem. let me see 1 sec

Answer 10

hrm kinda following this, it looks like the same thing just worked in a different way

did you come up with 223/11 for y0? maybe my math is wrong but it didn't accept 223/11 for the answer

Answer 11

dunno yet :) lets check

Answer 12

6z -5y = -40
-2z -2y = -61

y = (-366-80)/(-12-10) = 223/11 .... yep, so either the format is off, or the method is twisted in my head

Answer 13

hrm so frustrating.. there aren't any problems like this in our book

Answer 14

z = (-61(-5)-2(40))/(10+12) = 225/22 if so, but then the next step would be to plug it all into the plane equations to test

Answer 15

in essense, we have a picture of the zy plane taken at x=12

Answer 16

so the intersection of the zy instance at x=12 should result in the point they are looking for

Answer 17

what do you mean

Answer 18

i mean, you are prolly used to looking at the xy plane from the point of z=0 when you graph

Answer 19

there are a whole lot of other planes in front of and behind that xy plane at other z spots that may or maynot be the same depending on the equation of each plane in particular