I would really like explanation on how to do every question please. Thank you
1. Let P = (1, -1,3), Q = (0, 3, 5), and R = (-2, 5, 6). a) [4 pts] Find the distance from P to Q. b) [4 pts] True or False: There is a unique plane including the points P, Q, and R. (You must justify your conclusion in order to earn full credit.) c) [2 pts] Calculate PQ x PR. 2. a) [6 pts] Find the value of a so that the lines parametrizati t (1, 2, -3) and r2(t) = (-2, 0, 1) + t (4, 1, 0) intersect. b) [4 pts] Calculate the angle between these lines when they do intersect. 3. Consider the curve C parametrizationt, taint, }(2t)3/2) for t > 0. a) [10 pts] Find a parametrization L(t) for the tangent line to C at t = T. b) [10 pts] Calculate the arc length of C between t = 0 and t = 2T. 4. [8 pts] Evaluate the given limit, or show that it does not exist. lim (x,y) (0,0) 2+ 2 5. [12 pts] Let f(x, y) = In(x - y?). a) Give the domain of f in set-builder notation, and sketch it. b) Determine of - and of ay c) Find the linearization, L(x, y) of f at the point (1, 0).
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