Intersections of Two Planes Part 1

This lesson shows how two planes can exist in Three-Space and how to find their intersections. This is the first part of a two part lesson. This lesson was created for the Calculus and Vectors (MCV4U) course in the province of Ontario, Canada.

[AlRichards]

@TheCreamzy You need to eliminate 2 of the variables to get 2 equations that both have the same variable in them.. For example 2x - 3y = 12 and 5x + 8z = -7. You then set the common variable in both equal to t (parameter). So x = t and then you place the t in for x in the first 1 and solve for y. This gives you the parametric equation for y.
Then you place t in the other one for x and solve for z. This is the parametric equation for z.
Finally use x = t as the third parametric equation.

[jerrykuo]

a floor and a ceiling that shares the same points LOL. That made me laugh

[cata]

when you solve and get parametric equations could the answer differ depending on what you let t be ? so just like in the last lesson is there more than one answer to the question ?

[hafsaimtiaz]

Do we have to do further to solve paramatric equation

[ElDanteDelAnte]

Why did you substitute t for z as opposed to x or y? Does this strictly pertain to this instance where z is eliminated in the second subtraction of equations?

[blubberinghumdinger]

Really nice work. But just one thing. I thought it isn't possible to solve two equations that contain three variables each. Wouldn't you need another equation to figure out the values of x, y and z? Thanks a lot.

[hafsaimtiaz]

Is that example 2 non parallel planes??

[gregjacobsen]

At 6:35, -18-(-18) =-36, not 0, right??