Math 192 Final Cheatsheet - Unit Tangent Vector ( ) ( ) v t...

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Vector perpendicular to plane, v PQ PR = r uuur uuu v ; Area = (1/2) PQ PR P uuur uuur . Parallelepiped = ( ) A B C P Plane through P orthogonal to u , replace i , j , k , with x, y, and z, respectively. It is equal to the plane equation with a point (like P) inserted. Equation of line through P and Q P PQ P PQ p PQ x x t x y y t y z z t z P P = + = + = + uuur uuur uuur (where x PQ is the coefficient of x…; also where x p is the x-coordinate of point P) Distance PS n d n P = uuur r uur , where n is unit normal vector to plane. Projection PQ PS PQ proj PS PQ PQ PQ P = uuur uuur uuur uuur uuur uuur uuur Write PS as sum of a vector perpendicular to PQ and vector parallel to PQ Projection of PS over PQ (which is v-parallel) and (PS - v-parallel) [which is v-perpendicular]. Motion of Particle in Space
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Unformatted text preview: Unit Tangent Vector ( ) ( ) v t v t r r . Arc Length ( ) t t v t dt P r Multivariable functions and partial derivatives Vector-Valued functions- ( ) ( ) ( ) ( ) F t f t i g t j h t k = + + r r r Domain : set of points (x,y,z) in which f is well defined Range : set of values of f . Level curves : set f(x,y) = function equal to constant (ex.: 3 = x 2 + y 4 ). Same for level curves, except with 3-variables. Limits : Remember to substitute y = mx, or y = mx+b (under y = mx+b form), or y = mx n to find whether limit does not exist. Linearization : ( , ) ( , )( ) ( , )( ) x y L f x y f x y x x f x y y y = +-+-...
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