Question

Find the equation for the plane. Actually, I have the solution, I just need a little help understanding *why* it's the solution (see attached image).

Answer 1

is the given point in the stated line?

Answer 2

the line is given as:

x = 1+ ( 1)t
y = 2 + (-1)t
z = 0 + ( 1)t
^ ^ direction vector
^
anchor point

we are given 1 vector to play with, and need to create a second vector in order to cross and determine a normal vector to the plane

Answer 3

the vector from 1,2,0 to 1,0,1 define the needed vector

Answer 4

1-1 = 0
2-0 = 2
0-1 = -1
^
our other vector

so cross them

(1,-1,1) x (0,2,-1) = normal vector (a,b,c)

then just construct the plane equation

Answer 5

the graphing on the left side there does not appear to be accurate to the information in the problem tho

Answer 6

Ok, that makes more sense. Thank you!

Answer 7

yep, good luck :)