Question

Find the equation of the plane through (1,1,1) and containing the line which is the intersection of the planes x-y=2 and y-z=1

Answer 1

Can someone explaine to me how this is done

Answer 2

the line of intersecting planes is the cross of their direction vectors

Answer 3

First of all you need to understand how a plane is formed

Answer 4

<1,-1,0> x <0,1,-1> = intersection vector

Answer 5

How did you get that @amistre64?

Answer 6

i pulled of the normals from the plane eqs and crossed them

Answer 7

okay, so then you did the cross product

Answer 8

yes, cross the normals of the planes given to find the line asked for; then we work from that thing

Answer 9

okay, so the cross product gives us the vector: i+j+k

Answer 10

should i trust you for that? :)

Answer 11

the rest of the question is vague or mistyped

Answer 12

we need to find 2 points on this intersecting line tho

Answer 13

nope that is how it is written on my sample test

Answer 14

find a point that both intersecting planes have in common

Answer 15

x-y=2 and y-z=1

when x=0; y=-2

when y=-2; z=-3?

Answer 16

so the point (0,-2,-3) is on our intersecting line

we can use that and another point on the line to create 2 vectors to our (1,1,1) point

Answer 17

line:

x= 0+t
y=-2+t
z=-3+t

pick your favorite t

Answer 18

h

Answer 19

h aint a number that we can define a point with

Answer 20

oh i meant 6