7. Air traffic controllers use radar to keep track of the location of aircraft.

Question

7. Air traffic controllers use radar to keep track of the location of aircraft. The radar displays an aircraft's location in terms of the compass direction from the controller to the aircraft, and the horizontal distance along the ground between the two. In addition, the aircraft transmits its altitude to the controller automatically. Create a coordinate system by making east the positive x axis, north the positive y axis, and altitude the z axis. An aircraft is approaching at an altitude of 5.0 km, a horizontal distance of 35 km, and a bearing of 65 degree east of north. Write its position vector in rectangular coordinates. Write the vectors labeled A, B and C with rectangular coordinates. 9. Add the following vectors: (a) (12, 5) + (6, 3), (b) (-3. 8) + (6, -2); (c) (3, 8, -7) + (7, 2, 17); (d) ( a, b, c) + (d, e, f)

Explanation / Answer

7)
Z = 5 km

x = 35*sin(65) = 31.72 km

y = 35*cos(65) = 14.8 km

so position vector, r = xi + yj + zk

= (31.72 i + 14.8 j + 5 k)km

8) A = 3i + 2j

B = -i - 3j

C = -4i + 4j

9)

a) 18i + 8j

b) 3i + 6j

c) 10i + 10 j + 10k

d) (a+d)i + (b+e)j + (c+f)k

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