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

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Presentation transcript:

Eqaution of Lines and Planes

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

 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).

 Determine the size of the acute angle created between these two lines.  L 1: x = 2-5t y = 3+4t  L 2: x = -1+t  y = 2-4t

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

 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).

The Cartesian equation of a plane in R 3 is: Ax+By+Cz+D=0

 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)

 Sketch x=3, y=5, and z=6

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.

 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