 In this video, we will present the solution to question number 12 for the practice midterm exam number one for math 2270 We are asked to express a plane and our three that passes through the point negative 2 1 1 and is parallel to the plane spanned by 1 0 negative 1 and 3 negative 1 negative 2 We will express this plane as a vector equation and as parametric equations So we can see that we need a particular point on the plane. That's given to us right here So x naught is going to be the vector negative 2 1 1 We need to have two spanning vectors, which are told thus that because as our plan is parallel to these ones We get that you is going to equal 1 0 negative 1 and V is equal to 3 negative 1 negative 2 so our vector equation x is Basically going to look like the following we just take x naught plus s you plus TV Which maybe we expound upon that we get x 1 x 2 x 3 This is equal to negative 2 1 1 plus s You which is 1 0 negative 1 plus TV Which was given us 3 negative 1 negative 2 and So this gives us right here the vector equation the parametric equations then follow immediately from that We get that x 1 Equals negative 2 plus s plus 3 t x 2 Equals 1 Minus t because you have a zero s you don't see it there and then x 3 equals 1 Minus s minus 2 t and this will then give us the vector equation and the parametric equations for this plane in R3