CHEN 3005 Lecture Notes - Dot Product, Transpose, Unit Vector
8 Sep 2014
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3 types of #s we"ll use: scalar: mass (m), density ( ), temperature (t), pressure (p, vector: velocity (v), force (f), acceleration (a) When you have scalar * vector, same direction, just vector"s enlarged by *scalar. W = vwcos( vw) = magnitude of v * magnitude of w * cosine of angle between v and w. If v and w are parallel, then v . If v and w are perpendicular, then v . Cross product: v x w = vwsin( vw)nvw nvw is a unit vector normal to v and w. Chen transport page 1 nvw is a unit vector normal to v and w. Components of a vector unit vectors: i1, i2, i3. V = v1i1 + v2i2 + v3i3 = where j = 1,2,3the last expression = tensor. W = (v1i1 + v2i2 + v3i3) . (w1i1 + w2i2 + w3i3) only like terms give nonzero products (like i1 with i1etc)
