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If the vectors in the figure satisfy $ \mid u \mid = \mid v \mid = 1 $ and $ u + v + w = 0 $, what is $ \mid w \mid $?
Find the work done by a force $ F = 8i - 6j + 9k $ that moves an object from the point $ (0, 10, 8) $ to the point $ (6, 12, 20) $ along a straight line. The distance is measured in meters and the force in newtons.
Use intercepts to help sketch the plane.
$ 6x + 5y - 3z = 15 $
Use traces to sketch and identify the surface.
$ 4x^2 + 9y^2 + 9z^2 = 36 $
$ z^2 - 4x^2 - y^2 = 4 $
$ 3x^2 + y + 3z^2 = 0 $
