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 rA from the shuttle to satellite A has magnitude 3 km and direction cosines cosx=0.768, cosy=0.384, cosz=0.512. The vector rB from the shuttle to satellite B has magnitude 7 km and direction cosines cosx=0.743, cosy=0.557, cosz=0.371.

Part A

What is the distance between the satellites?

Solution

rA= 3( cos0xi + cos0yj+cos0zk)
=2.304i +1.152j+1.536k

rB=7( cos0xi + cos0yj+cos0zk)
=5.201i+3.899j-2.597k

the distance between them is:
sqrt((2.304 -5.201)^2 + (1.152- 3.899)^2 + (1.536 + 2.597)^2)
= sqrt(8.392609 +7.546009 + 17.081689 )
= sqrt(33.020307)
=5.746