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Chapter 8

Chapter 8. Eqaution of Lines and Planes. Determining the vector/parametric equation of a line in R 2. Determine the vector and parametric equations of a line that contains the point (2,1) and (-3,5). Determining the Cartesian Equation of a Line in R 2.

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Chapter 8

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  1. Chapter 8 Eqaution of Lines and Planes

  2. Determining the vector/parametric equation of a line in R2 • Determine the vector and parametric equations of a line that contains the point (2,1) and (-3,5).

  3. Determining the Cartesian 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).

  4. Determining the Angle Between Two Intersecting Lines • 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

  5. Symmetric Equations of Lines (R3) • Convert the Line r=(6,4,1)+t(3,9,8), teR to Symmetric Equation Form

  6. Determining the Vector/Parametric Equation of Planes

  7. Determining the Vector/Parametric Equation of Planes Contd. • 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).

  8. The Cartesian Equation of A Plane The Cartesian equation of a plane in R3 is: Ax+By+Cz+D=0

  9. The Cartesian Equation of A Plane Contd. • 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)

  10. Sketching Planes in R3 • Sketch x=3, y=5, and z=6

  11. Thinking and Inquiry 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.

  12. 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

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