1 11.3: Torque and Cross-ProductDefinitions: The torque of a vector F about a vector rThe cross-product of vectors a and b:Note that a × b is orthogo nal to both a and b: If a = ha1, a2, a3i, b = hb1, b2, b3i, and a × b =hx1, x2, x3i, then we have:The cross-product of vectors a and b (ONLY in R3) is given bya × b =1NOTES:1. Simple calculation method:2. Geometric significance:3. |a × b| =4. Useful Properties (all lis ted on p668):Examples:Find a × b if a = i + 2j − k and b = 3i − j + 7k2Given the points P (1, 0, −1), Q(2, 4, 5), and R(3, 1, 7) find a vector orthogonal to the plane containingthese points.Find the are a of △P QR.3Find 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 a pplied to a nut with a force of 80N (See pic ture below). Because o f limitedspace, the force must be exerted straight upward. How much torque is applied to the
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