Astronauts on the space shuttle use radar to determine the m

Astronauts on the space shuttle use radar to determine the magnitudes and direction cosines of the position vectors of two satellites A and B. The vector r_A from the shuttle to satellite A has magnitude 2 km and direction cosines cos theta_x, = 0.768, cos theta_y = 0.384, cos theta_z = 0.512. The vector r_B from the shuttle to satellite B has magnitude 4 km and direction cosines cos theta_x = 0.743, cos theta_y = 0.557, cos theta_z = -0.371. What is the distance between the satellites?

Solution

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