Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point P= (0,4,8). The ground is modeled by the plane z+y+z=0 and the light casts a shadow of the line segment onto the ground. Give a parametrization of the shadow.

Q: Find three different pairs of parametric equations for the line segmentthat starts at (0, 0) and…

A: Direction ratio is = (6-0, 6-0)= (6,6) That is equivalent to (1,1) , (2,2) and (3,3)

Q: Find parametric equations for the line in which the planes, x+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A: Given, The equation of intersecting planes, x+2y-2z=5 and 5x-2y-z=0.   We have, x + 2y = 2z + 5 and…

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

A:

Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A:

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

A: