L ESSON 26 – E QUATIONS OF P LANES September 4, 2013 Fernando Morales

P EER I NSTRUCTION Coincident: 1. Occuring together in space or time 2. In agreement or harmony 3. The two lines have all equal points Answer: If they are scalar multiples of each other, then they are coincident. In this case since we can multiply all the terms in first equation by six, we obtain the second equation. Hence all points will be equal between the two lines.

M OVE A ROUND ! Go around the classroom and answer the questions on the wall. Use technology to assist you in checking the answers.

P EER I NSTRUCTION How can we define a line in two-space? How can we define a line in three-space? [C] In both cases all we need is either two points or a point and a direction vector.

P EER I NSTRUCTION How do we uniquely define a plane in three- space? [C] To uniquely define a plane in three-space all we need is either three non-collinear points or a point and two non-parallel direction vectors.

R EQUIRED B EFORE N EXT C LASS Section 8.2 # 1, 2, 3, 10, 11 Read Section 8.3 On Pg. 445 Complete the Investigation: How is the Normal Vector to a Plane Related to the Scalar Equation of a Plane? (all six, have it prepared to show me Thursday)

W HAT DO THE POINTS HAVE IN C OMMON ? W RITE A P OSSIBLE E QUATION FOR THE P LANE ?