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).