Find the normal form and vector for of the equation of the plane that passes through P1 = (0,-2,5), P2 = (1, -1, 1), and P3 = (-1,2,0) (Hint: P1P2 x P1P3 os a normal vector for the plane)

Question

turingtest · Answer

how far have you gotten?

anonymous · Answer

Not really far, it is really hard for me, my teacher is from asia and very hard to understand him so I can only learn from his notes. It isn't very helpful, but I need somebody to explain it to me and show me how to go through it step by step if possible.

turingtest · Answer

typo*$$\vec v_1=p_2-p_1$$$$\vec v_2=p_3-p_1$$

turingtest · Answer

can you find these vectors?

anonymous · Answer

Umm, would it just be v1 = (-1, 1, -4) and v2 = (-1, 4, -5) ?

turingtest · Answer

the first one should be v1=(1,1,-4)
but yeah, that's it...
let me draw it so you can see what we're actually doing more clearly

turingtest · Answer

we are given 3 points

turingtest · Answer

|dw:1348808751241:dw|we have a plane in space with some rectangular coordinate system, and 3 known point in the plane

turingtest · Answer

each point on the plane is associated with a position vector|dw:1348808892122:dw|we can add and subtract these position vectors at will.
If we subtract two position vectors to points in the same plane, the vector we get will lie $in$ that plane (think about that...)