Astronauts on the space shuttle use radar to determine the magnitudes and direct

Question

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?

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?

Explanation / Answer

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

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