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 (Ax + By + C = 0 or y = mx + c) Eg. –x + 2y – 10 = 0 or y = 1/2 x + 5

Vector Equation of a Line in 2D

• Vector Equation

Vector Equation of a Line in 2D

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)

Pop Quiz #1

Write a vector equation of the following:

1. m = [3, 1], P0 (2, 7)

2. A (1, 7), B (4, 10)

Parametric Equations

• From ,

• Separate x and y

Parametric Equations

Normal Vector

• Perpendicular -> Negative Reciprocal Gradient

Pop Quiz #2

Write the vector equation, the scalar equation and the normal vector of the following vector

x = 3 + 5ty = 9 + 7t

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)

Equations of Lines in 3D

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

Suggested Questions

P. 438 # 20 # 23 # 24 a)