2. The volume V of a tetrahedron is one-third the distance from a vertex to the...

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2. The volume V of a tetrahedron is one-third the distance from a vertex to the opposite face, times the area of that face. (a) Find a formula for the volume of a tetrahedron in terms of the coordinates of its ver- tices P, Q, R. and S. (b) Find the volume of the tetrahedron whose vertices are P(1, 1, 1), Q(1, 2, 3), R(1, 1, 2), and S(3,-1,2). Q P S R 2. The volume V of a tetrahedron is one-third the distance from a vertex to the opposite face, times the area of that face. (a) Find a formula for the volume of a tetrahedron in terms of the coordinates of its ver- tices P, Q, R. and S. (b) Find the volume of the tetrahedron whose vertices are P(1, 1, 1), Q(1, 2, 3), R(1, 1, 2), and S(3,-1,2). Q P S R