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Two lines have equations L1: x=3t+ 1,y = 3,z=-t+2, tE R and L2: x=2s+3,y =s+1,z=3s-2, sER. Determine points P and Q if P is a point on L1 and Q is a point on L2 and PQ is perpendicular to both lines.

11. Show that the lines L1: (4,-7,2) + s(-2,6,2) , sE R and L2: (-5,8,-13) + t (-3,8, 1), tER lie on the plane 5x+2y-z-4=0.

What would you expect to be the distance between the parallel lines x + 4y - 2=0 and -3x - 12y +6 = 0? Use the distance formula to determine the distance and interpret your results.

Does the point of intersection between L1: (4,9,2) + s (1,-1,-1), s E R and L2: (2, 11,4) + t(5,-3,-4), te R lie on the plane 3x - 2y + 3z + 4 = 0?

Determine values of k for which the system has one solution, infinite solutions, and no solutions.

-5x + y + 2z= -1

3x+y+2z=1

6x+2y+k^2=k