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4 Cross product as a matrix multiply . . . . . 5 The cross product is distributive over sums . . 4 Solving vector equations . . . . . . . . . . 6 Vector triangles and the laws of sines and cosines . 7 Existence, uniqueness, and geometry . . . . 5 Equivalent force systems . . . . . . . . . . 8 means add . . . . . . . . . . 10 A “wrench” can represent any force system . . 6 Center of mass and gravity . . . . . . . . . . 11 Like , the symbol also means add .

Sometimes the motion associated with deformation is important in itself, say you would like a building to not sway too much in the wind. And sometimes the larger net transport motion is of interest; for example we would like all points on a plane to travel about the same large distance from New York to Bangalore. Really, deformation and motion are not distinct topics, both involve keeping track of the positions of points. The distinction we have made is for simplicity. Trying to simultaneously describe deformations and large motions is just too complicated for beginners to understand and too complicated for most engineering practice.

Drawing vectors ✯ In fig. 1 on page 37, the magnitude of ❆ was used as the drawing length. But drawing a vector using its magnitude as length would be awkward if, say, ✯ we were interested in vector ❇ that points Northwest and has a magnitude ✯ of ✷ meters. To well contain ❇ in a drawing would require a piece of paper about 2 meters square (each edge the length of a basketball player). This situation moves from difficult to ridiculous if the magnitude of the vector of interest is ✷ km and it would take half an hour to stroll from tail to tip dragging a purple crayon.

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