THE VECTOR EQUATION OF A PLANE parametric form

THE VECTOR EQUATION OF A PLANE (parametric form) Learning Outcomes: • Know when three vectors are coplanar • Be able to write a plane in vector form given two nonzero, non-parallel vectors which lie in the plane.

• Know when three vectors are coplanar ØYou can write one of the vectors as a sum of multiples of the other two. Explanation

THE VECTOR EQUATION OF A PLANE (parametric form) Explanation • If a, b and c are coplanar • Be able to write a plane in vector form given two non-zero, non-parallel vectors which lie in the plane. 3 cop lanar vector s

Example 1: a) Find the equation of the plane, in vector form, which contains points A(1, 2, -1), B(-2, 3, 2) and C(4, 5, 2) Page b) Find the point on the plane corresponding 62 to the parameter values t = 2, u = 3 ØFind position vectors for A, B anc C ØFind equation Page 63 b) t = 2, u = 3 Ex 8 1 NOT UNIQ UE

Example 3: Find the cartesian equation of the plane whose vector equation is Page 62 ØRewrite in terms of t and u ØFind normal ØFind k ØWrite equation Page 63 Ex 8 4

Example 2: What conditions must be met so that P(-8, 9, 14) lies on the plane with vector equation P age 62 ØIf P lies on the plane then ØWrite equations to be solved ØFind t and u Page 63 Ex 8 6, 7 For P(-8, 9, 14) to lie on the given plane we must have t = 4 and u = 1

Example 3 a: Find a vector equation for the plane containing Page A(1, 1, 1) with normal vector 63 ØIf A lies on the plane then ØWrite equations to be solved ØFind For P(-8, 9, 14) to lie on the given plane we must have t = 4 and u = 1