Suppose that you are climbing a hill whose shape is given by $z = 813 - 0.03 x^2 -0.06 y^2$, and that you are at the point (30, 90, 300).
In which direction (unit vector) should you proceed initially in order to reach the top of the hill fastest?
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If you climb in that direction, at what angle above the horizontal will you be climbing initially (radian measure)?