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Equation of a Plane

Equation of a Plane. November 2007. Homework Quiz. Page 40 Page 41 7 d) 12 a) Page 42 Page 43 14 c) 16 b). The Equation of a Plane. In 3-dimensional space, the equation of a plane is given by: A x + B y + C z + D = 0

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Equation of a Plane

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  1. Equation of a Plane November 2007

  2. Homework Quiz • Page 40 Page 41 7 d) 12 a) Page 42 Page 43 14 c) 16 b)

  3. The Equation of a Plane • In 3-dimensional space, the equation of a plane is given by: • Ax + By + Cz + D = 0 • as long as A, B, and C, are not simultaneously zero, and A, B, C, D € R.

  4. To find the equation of the plane that contains the three points: • E = (10, 1, 1) • F = (2, -2, 2) and • G = (12, 7, 3)

  5. Divide the general equation by A so that the coefficient of x is 1. • Rewrite this equation as x + Py + Qz+ R = 0

  6. Substitute the given values of (x, y, z) into rewritten equation. (10, 1, 1) → 10 + P + Q + R = 0 (2, -2, 2) → 2 – 2P + 2Q + R = 0 (12, 7, 3) → 12 + 7P + 3Q + R = 0

  7. Rearrange • P + Q + R = -10 • -2P + 2Q + R = -2 • 7P + 3Q + R = -12

  8. Solve for P, Q and R. P = Q = R =

  9. 6. Substitute back into “rewritten” equation.

  10. 7. To write this equation in General Form, multiply through by largest denominator.

  11. Find the plane containing each of the following sets of points: • (2, 4, 7), (1, 0, 5), (-2, -3, 8) b) (1, -2, 3) (4, 12, 0), (1, 3, -2)

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