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1. (7 pts)
Alice and Bob are trying to lift a rock that weighs 60 lb. They each
exert a force represented by the vectors a and b. With respect to
the standard rectangular coordinate system, a = ⟨ −5, 20⟩ while b
has magnitude F and makes an angle of 30 with the positive x-axis.
How great must F be in order for them to lift the rock vertically? Note
that the forces in the horizontal direction don’t need to be balanced.
2. (10 pts)
Consider the surface defined in cylindrical coordinates by
z = r
2 − 2r cos θ + 1.
a) (6 pts) Write an equation for the surface in rectangular coordinates.
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