2. (a) Draw and parametrize the circle of radius two centered at (1, −1, 1) and lying on the plane x+y+z= 1. Hint: find two orthogonal unit vectors which are parallel to the plane.

1) Find the distance from the point (1, 2, 3) to the (a) XZ plane (b) Z axis

Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to the plane 2x-1y-5z=1. Use 't' as your variable, t=0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. a)X=? b)y=? c)z=?

Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the distance separating them