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8.1 Equations of Lines in 2D and 3D

8.1 Equations of Lines in 2D and 3D. MCV4U Grade 12 Calculus and Vector. Vector Equation of a Line in 2D. So far: Scalar Equation (A x + B y + C = 0 or y = mx + c ) Eg . – x + 2 y – 10 = 0 or y = 1/2 x + 5.

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8.1 Equations of Lines in 2D and 3D

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  1. 8.1 Equations of Lines in 2D and 3D MCV4U Grade 12 Calculus and Vector

  2. Vector Equation of a Line in 2D • So far: Scalar Equation (Ax + By + C = 0 or y = mx + c) Eg. –x + 2y – 10 = 0 or y = 1/2 x + 5

  3. Vector Equation of a Line in 2D • Vector Equation

  4. Vector Equation of a Line in 2D

  5. Vector Equation of a Line in 2D Example: Write a vector equation for the line through the points A (1, 4) and B (3, 1)

  6. Pop Quiz #1 Write a vector equation of the following: 1. m = [3, 1], P0 (2, 7) 2. A (1, 7), B (4, 10)

  7. Parametric Equations • From , • Separate x and y

  8. Parametric Equations

  9. Normal Vector • Perpendicular -> Negative Reciprocal Gradient

  10. Pop Quiz #2 Write the vector equation, the scalar equation and the normal vector of the following vector x = 3 + 5t y = 9 + 7t

  11. Equations of Lines in 3D • Can be defined by a vector equation or parametric equations • Cannot be defined by a scalar equation as a scalar equation is a PLANE (8.2) • Same structure as 2D but one more component (z)

  12. Equations of Lines in 3D

  13. Pop Quiz #3 Given the points A (3, 4, -5) and B (9, -2, 7), write a vector equation and the parametric equations of the line through A and B

  14. Suggested Questions P. 438 # 20 # 23 # 24 a)

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