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Additional info for Schaum's Outline of Advanced Mathematics for Engineers and Scientists
Five. seventy one. If r = a cos at + b sin at, the place a and b are any consistent noncollinear vectors and « is a continuing scalar, end up that (a) r X five. seventy two. If A = X2i -yj + xzk, B = yi + xj- xyzk (6) d[A • (B X C)] on the aspect (1, -1,2). and C = i - yj + xszk, locate ( five. seventy three. If R five. seventy four. If A is a differentiate functionality of u and |A(tt)| = 1, turn out that dA/du is perpendicular to A. five. seventy five. enable T and N denote respectively the unit tangent vector and unit imperative basic vector to an area curve r = i(u), the place r(u) is thought differentiate. outline a vector B = T X N known as the unit binormal vector to the distance curve. turn out that a ) a n d on the aspect those are known as the Frenet-Serret formulation. In those formulation ok is named the curvature, T is named the torsion; and the reciprocals of those, p — l//c and a = I/T, are known as the radius of curvature and radius of torsion respectively. GRADIENT, DIVERGENCE AND CURL five. seventy six. If U, V, A, B have non-stop partial derivatives end up that: (a) five. seventy seven. If