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.

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