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Astronauts on the space shuttle used radar to determine the magnitudes and direction cosines of the position vectors of two satellites A and B. The vector rA from the shuttle to satellite A has magnitude 2 km and direction cosines cos?x = 0.768, cos?y = 0.384, and cos?z = 0.512. The vector rB from the shuttle to satellite B has magnitude 4 km and direction cosines cos?x = 0.743, cos?y = 0.557, and cos?z = -0.371. What is the angle between the two vectors rA and rB?

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