need help calc 3!!!! life saveeer?
1) Find the volume of the tetrahedron with vertices (-4,-1,-4),(-8,-2,-2) ,(1,-3,-6),and (-9,-1,-3).
2) Find the volume of the parallelepiped with one vertex at (-2,-3,-5) and adjacent vertices at (2,-3,-1) , (-9,-7,-6) and (0,-6,-9)
3) A wrench 0.7 meters long lies along the positive -axis, and grips a bolt at the origin. A force is applied in the direction of <0 ,-5,-5> at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt.
4) A bicycle pedal is pushed straight downwards by a foot with a 41 Newton force. The shaft of the pedal is 20 cm long. If the shaft is pi/4 radians past horizontal, what is the magnitude of the torque about the point where the shaft is attached to the bicycle?
5) Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (5, 1, -2), Q = (8, 4, 1), and R = (8, 4, 2).
thats a whole lot of homework down there.
I ll help you with first question. you need to calculate the edge of the tetrahedron. do it using euclidean distance between any two vertices.
the use V = sqrt(2)/12 * a^3
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