Astronauts on the space shuttle used radar to determine the magnitudes and direc

Question

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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Explanation / Answer

The direction cosines of the vectors along rA and rB are the components of the unit vectors in these directions uA (i.e., D cos x i C cos y j C cos z k, where the direction cosines are those for rA ). Thus, through the definition of the dot product, we can find an expression for the cosine of the angle between rA and rB = cos D = cos xA cos xB + cos yA cos yB + cos zA cos zB . =>cos D = 0.594 =>D = 53.5Degrees

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