Example: Find a parametrization of (or a set of parametric equations for) the plane \begin{align} x-2 y + 3z = 18. working out the parametric equation of a plane given 3 points Watch Announcements ... We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun This second form is often how we are given equations of planes. Calculus and Vectors – How to get an A+ 8.4 Vector and Parametric Equations of a Plane ©2010 Iulia & Teodoru Gugoiu - Page 2 of 2 Ex 4. Notice that if we are given the equation of a plane in this form we can quickly get a normal vector for the plane. Thus, to find an equation representing a line in three dimensions choose a point P_0 on the line and a non-zero vector v parallel to the line. Parametric curves have a direction of motion When plotting the points of a parametric curve by increasing t, the graph of the function is traced out in the direction of motion. Example: Write the parametric equations of the line y = (-1/2)x + 3 and sketch its graph. Example showing how to parametrize a plane. Vector Equation of the Plane To determine the equation of a plane in 3D space, a point P and a pair of vectors which form a basis (linearly independent vectors) must be known. Equations of Lines and Planes Lines in Three Dimensions A line is determined by a point and a direction. parallel to the line. Can you please explain to me how to get from a nonparametric equation of a plane like this: $$ x_1−2x_2+3x_3=6$$ to a parametric one.