1 11 3 Torque and Cross Product Definitions The torque of a vector F about a vector r The cross product of vectors a and b Note that a b is orthogonal to both a and b If a ha1 a2 a3 i b hb1 b2 b3 i and a b hx1 x2 x3 i then we have The cross product of vectors a and b ONLY in R3 is given by a b 1 NOTES 1 Simple calculation method 2 Geometric significance 3 a b 4 Useful Properties all listed on p668 Examples Find a b if a i 2j k and b 3i j 7k 2 Given the points P 1 0 1 Q 2 4 5 and R 3 1 7 find a vector orthogonal to the plane containing these points Find the area of P QR 3 Find the volume of the parallelipiped whose corner is formed by the vectors a h2 3 2i b h1 1 0i and c h2 0 3i A wrench 0 5m long is applied to a nut with a force of 80N See picture below Because of limited space the force must be exerted straight upward How much torque is applied to the nut 4
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