Question

Did I answer this question right?

Answer 1

4) The vector v = 9i -14j +k lies in the plane, P, that contains the point P = (2, 1, 3). Determine an equation for the plane P.
We have all we need to create an equation for the plane. A point and a direction vector.
a(x - x₁) + b(y - y₁) + c(z - z₁)  9(x – 2) -14(y – 1) + (z – 3)  9x – 14y + z = 7

Answer 2

Or is a b and c supposed to come from normal vector? So I need to find the normal vector somehow?

Answer 3

givent a point and a vector, there is no way to define a plane. we need 2 vectors that will at least span the plane and a 3rd vector that is orthogonal to the other 2

Answer 4

from geometry, we should recollect that it takes at least 3 points to establish a plane with; 2 point to form a line, and a 3rd point not on the line

Answer 5

what you have established here by applying this vector to the point is to define a plane that is perpendicular to the given point; since you are using the vector as a normal instead of a vector in the plane