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Planes in Space

Planes in Space. z. Equation of a Plane. y. x. z. Equation of a Plane. y. x. z. Equation of a Plane. y. x. z. Equation of a Plane. y. x. z. Equation of a Plane. y. b. x. z. Equation of a Plane. c. y. x. z. Equation of a Plane. y. x. z. Equation of a Plane. n. P.

terrence-quinones
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Planes in Space

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  1. Planes in Space

  2. z Equation of a Plane y x

  3. z Equation of a Plane y x

  4. z Equation of a Plane y x

  5. z Equation of a Plane y x

  6. z Equation of a Plane y b x

  7. z Equation of a Plane c y x

  8. z Equation of a Plane y x

  9. z Equation of a Plane n P y x

  10. z Equation of a Plane P(x0,y0,z0) Q(x,y,z) n=ai+bj+ck r=(x-x0)i+(y-y0)j+(z-z0)k n Q r P r Q y x

  11. z Equation of a Plane P(x0,y0,z0) Q(x,y,z) n=ai+bj+ck r=(x-x0)i+(y-y0)j+(z-z0)k n Q r P r Q y Vector Equation x Scalar Equation

  12. z Equation of a Plane P(x0,y0,z0) Q(x,y,z) n=ai+bj+ck r=(x-x0)i+(y-y0)j+(z-z0)k n Q r P r Q y Vector Equation x Scalar Equation

  13. z Equation of a Plane P(x0,y0,z0) Q(x,y,z) n=ai+bj+ck r=(x-x0)i+(y-y0)j+(z-z0)k n Q r P r Q y Vector Equation x Scalar Equation

  14. Examples • Find the equation of the plane through (1,1,2), (3,2,-1) and (4,2,-1). • Find the equation of the plane through (2,-1,3) and parallel to 3x – y + 4z =12.

  15. Intercepts of a Plane • Find the intercepts of the planes 2x – 3y + z = 6 4y + 2x = 8 z = 3 • Sketch the planes. • Find the normals to the planes.

  16. Examples z • Find the equation of the plane pictured. 4 y 5 3 x

  17. Graphing Planes Sketch the following planes: (a) 3x - 2y + z = 6 (b) z + 2y = 4 (c) y = 2

  18. Angle Between Planes • Find the angle between the two planes 2x – 3y + 4z = 6 and x + 2y – 3z = -1

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