Problem 78. Find the projection of the vector v = (2, 1, 4) onto the plane given by the equation x - 27 + 52 =0. Problem 79. Find the projection of the vector v = (2, 1, 4) onto the plane S passing through the following three points in space (0,0,0), (1, 1, 1), (1, -1, 1) . Problem 80. Find the point on the plane S given by the equation closest to (2, 1, 4). Problem 81. Consider two planes S, and S, in R' given by the equations cty+z=0 and cty+z=1 respectively. Do they intersect? Problem 82. Find the volume of the parallelepiped spanned by the vectors u = (1, 2,3), v = (-1, 1, 2) and w = (2, 1, 4). Problem 83. Is the line through (-4, -6, 1) and (-2,0, -3) parallel to the line through (10, 18, 4) and (5, 3, 14)