Cal2 Test 1

Cal2 Test 1 - Eqn. of a sphere in 3D: (x-x1) + (y-y1) +...

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Eqn. of a sphere in 3D: (x-x1) ² + (y-y1) ² + (z-z1) ² = r ² Vector quantities: displacement, velocity, acceleration, force Non-vector quantities: duration, temperature, energy, mass SAS: Law of Cosines: c ² = a ² + b² - 2ab cos C Vector i: horizontal Given |A| and Θ : x = |A| cos Θ, y = |A| sin Θ Cross product is not commutative A x B is perpendicular A dot B is parallel i x j = k j x i = -k i x i = 0 j x k = i k x j = -i k x i = j i x k = -j A x B (3D) : (A2 B3 – A3B2)i + (A3 B1 – A1 B3)j + (A1 B2 – A2 B1)k If A x B = 0: parallel. If A dot B = 0: perpendicular. x y z xo yo zo Find a line || <3,1,4> and contains (0,5-5) Parametric: x = xo + ta 3 (x – xo = ta) t = x/3 x/3 = 5 - y y = yo + tb 5-t (y – yo = tb) t = 5 – y x/3 = (z+5)/4 z = zo + tc -5+4t| (z – zo = tc) t = (z + 5)/4 ^^Symmetric^ vector PoP = x – xo, y – yo, z – zo
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This note was uploaded on 04/21/2008 for the course MA 126 taught by Professor Moore during the Fall '08 term at Alabama.

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