8.1 Equations of Lines in 2D and 3D
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Transcript of 8.1 Equations of Lines in 2D and 3D
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8.1 Equations of Lines in 2D and 3D
MCV4U
Grade 12 Calculus and Vector
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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
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Vector Equation of a Line in 2D
• Vector Equation
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Vector Equation of a Line in 2D
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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)
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Pop Quiz #1
Write a vector equation of the following:
1. m = [3, 1], P0 (2, 7)
2. A (1, 7), B (4, 10)
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Parametric Equations
• From ,
• Separate x and y
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Parametric Equations
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Normal Vector
• Perpendicular -> Negative Reciprocal Gradient
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Pop Quiz #2
Write the vector equation, the scalar equation and the normal vector of the following vector
x = 3 + 5ty = 9 + 7t
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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)
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Equations of Lines in 3D
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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
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Suggested Questions
P. 438 # 20 # 23 # 24 a)