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Problem 78. Find the projection of the vector v = (2, 1, 4) onto the plane given by the equation x - 2y + 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 a = 2 closest to (2, 1, 4). Problem 81. Consider two planes S, and S2 in R3 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) ? Problem 84. Is the line through (-2, 4, 0). and (1, 1, 1) perpendicular to the line through (2, 3, 4) and (3, -1, -8)