Astonauts on the space shuttle use radar to determine themagnitudes and directio

Question

Astonauts on the space shuttle use radar to determine themagnitudes and direction cosines of the position vectors of twsatellites A and B. The vector rA from the shuttle tosatellite A has magnitude 2km and direction cosinescosx= 0.768, cosy= 0.384, andcosz= 0.512. The vector rB has amagnitude of 4km, and direction cosines cosx=0.743, cosy= 0.557, and cosz=-0.371. What is the distance between the satellites? attemption: I found rAB and its magnitude, which made e findeAB. but now, have no idea what I am supposed to do withthe given magnitude of A and B. or I guess I did everythingwrong!! Astonauts on the space shuttle use radar to determine themagnitudes and direction cosines of the position vectors of twsatellites A and B. The vector rA from the shuttle tosatellite A has magnitude 2km and direction cosinescosx= 0.768, cosy= 0.384, andcosz= 0.512. The vector rB has amagnitude of 4km, and direction cosines cosx=0.743, cosy= 0.557, and cosz=-0.371. What is the distance between the satellites? attemption: I found rAB and its magnitude, which made e findeAB. but now, have no idea what I am supposed to do withthe given magnitude of A and B. or I guess I did everythingwrong!!

Explanation / Answer

rA = 2 (cosx i + cosyj + cosz k) km = 2 (0.768 i + 0.384 j + 0.512 k)km = (1.536 i + 0.768 j + 1.024 k) km rB = 4 (cosx i + cosyj + cosz k) km = 4 (0.743 i + 0.557 j - 0.371 k)km = (2.972 i + 2.228 j - 1.484 k) km rAB = rB - rA = (1.436 i +1.460 j - 2.508 k) km the distance = (1.4362 + 1.4602 +2.5082) = 3.238 km

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