A tracking station lies at the origin of a

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coordinate system with the x-axis due east,
the y-axis due north and the z-axis vertically
upwards. Two aircraft have coordinates
(20,25,11) and (26,31,12) relative to the
tracking station.
a Find the distance between the two
aircraft at this time.
b The radar at the tracking station has a
range of 40 km. Determine whether it
will be able to detect both aircraft.

A tracking station lies at the origin of a

Jawaban:

a. dist = √[(26-20)²+(31-25)²+(12-11)²]

= √(36+36+1)

= √73

b. dist 1st aircraft from O

= √(20²+25²+11²)

= √1146

≈ 34 km

34 < 40 ==> within radar

dist 2nd aircraft from O

= √(26²+31²+12²)

= √1781

≈ 42 km

42 > 40 ==> outside radar