Chase Berry csb4319

Week 1 1.2.8

Find an equation and a parametric representation for the plane passing through the points (1,0,1),(2,3,1), and (5,4,5).

Solution: As in example 6, parallel vectors between points on a plane make vectors parallel to that plane. I chose the point (1,0,1) to subtract for the other points because it is easiest to use.

The parametric representation is constructed using s as a scaler for u and using t as a scaler for v. The third part is the common point used in determining the vectors u and v.

To find the equation of a plane, you need a vector perpendicular to it. One can be found by taking the cross product of u and v.

To find the constant, use the dot product between the common point of the vectors and the perpendicular vector.

The equation of the plane is then 12x-4y+8z=4. This is equal to 3x-y-2z=1