1. MCV4U1 8.5 - The Intersection of 3 Planes Types of Intersection: 1.) Parallel Normals a) Three Parallel and Distinct Planes b) Two Parallel and Distinct, One is NOT c) Three Coincident Planes d) Two Coincident, One is Parallel and Distinct e) Two Coincident, One is NOT n 1 = jn 2 = k n 3 And D 1 ≠ jD 2 ≠ kD 3 n 1 = jn 2 ≠ k n 3 And D 1 ≠ jD 2 D 1 = jD 2 = kD 3 D 1 = jD 2 ≠ kD 3 D 1 = jD 2 And n 1 = jn 2 = k n 3 n 1 = jn 2 ≠ k n 3 ***Find the line of intersection using Gaussian Elimination***

2. Types of Intersection: 2.) Non-Parallel Normals a) Intersect at a Point b) Intersect along a line c) Triangular Prism ***Solve using Gaussian Elimination*** Bottom row results in [0 0 0 0] ***Solve using Gaussian Elimination*** Bottom row results in [0 0 0 #]

3. a) x + 2y + 3z = -4 2x + 4y + 6z = 7 x + 3y + 2z = -3 b) x + 2y + 3z = -4 2x + 4y + 6z = 7 3x + 6y + 9z = 5 c) x + 3y - z = -1 - x - 3y + z - 1 = 0 4x + 12y - 4z = -4 d) x + 2y + 3z = -4 x - y - 3z - 8 = 0 2x + y + 6z + 14 = 0 Ex.) Determine the intersection of the following sets of planes. Provide a geometric interpretation for each example.

4. e) x + 2y + 3z = -4 x - y - 3z = 8 x + 5y + 9z = -16 f) x + 2y + 3z = -4 x - y - 3z = 8 x + 5y + 9z = -10 Ex.) Determine the intersection of the following sets of planes. Provide a geometric interpretation for each example.

5. Homework:p. 309 # 7, 8, 9

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