Chapter 8Eqaution of Lines and Planes

Determine the vector and parametric equations of a line that contains the point (2,1) and (-3,5).

Determining the vector/parametric equation of a line in R2

 

To determine the Cartesian equation of a line, write out the general equation and then use the direction vector perpendicular to that of the line and sub the X and Y values (of the normal vector) as the A and B coefficients respectively.

Ax + By + k = 0 Determine the Cartesian equation of a line

with a normal vector of (4,5) passing through the point A(-1,5).

Determining the Cartesian Equation of a Line in R2

Determine the size of the acute angle created between these two lines.

L1: x = 2-5t

y = 3+4t

L2: x = -1+t y = 2-4t

Determining the Angle Between Two Intersecting Lines

Convert the Line r=(6,4,1)+t(3,9,8), teR to Symmetric Equation Form

Symmetric Equations of Lines (R3)

Determining the Vector/Parametric Equation of Planes

Determine the equation of the plane that contains the point P(-1,2,1) and the line

r=(2,1,3)+s(4,1,5) S∊R

Determine the vector equation for the plane containing the points P(-2,2,3), Q(-3,4,8), R(1,1,10).

Determining the Vector/Parametric Equation of Planes Contd.

The Cartesian equation of a plane in R3 is:

Ax+By+Cz+D=0

The Cartesian Equation of A Plane

Determine the Cartesian equation of the plane containing the point (-1,1,0) and perpendicular to the line joining the points (1,2,1) and (3,-2,0)

The Cartesian Equation of A Plane Contd.

Sketch x=3, y=5, and z=6

Sketching Planes in R3

The plane with the equation r=(1,2,3)+m(1,2,5)+n(1,-1,3) intersects the y and z axis at the points A and B respectively. Determine he equation of the line that combines these points.

Thinking and Inquiry

Determine the Cartesian equation of the plane that passes through the points (1,4,5) and (3,2,1) and is perpendicular to the pplane 2x-y+z-1=0

Thinking and Inquiry