Given the points P(1, 2, 3), Q(1,−1, 2) and R(2, 1, 0):
Determine the parametric vector equation of the plane through the points P, Q and R. Verify that any x satisfying this equation has coordinates which also satisfy the Cartesian equation.
Given the points P(1, 2, 3), Q(1,−1, 2) and R(2, 1, 0):
Determine the parametric vector equation of the plane through the points P, Q and R. Verify that any x satisfying this equation has coordinates which also satisfy the Cartesian equation.
Use the definition of a plane by a normal vector and a point.
$\displaystyle n*(x-x_0)=0$, where * means dot product. The only thing to do is find the normal vector. To find this use the three points to construct two vectors, then take the cross product of them.