# Displacement of airplanes in opposite directions.

An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by vector A, which has the magnitude 220km and points in a direction 32(degrees) north of west. The displacement from the control tower to plane 2 is given by the vector B, which has a magnitude of 140km and points 65(degrees) east of north. Find the magnitude and direction of vector C.

I understand that it needs to be broken up into its components, but I am unable to get the answer (320km @ 10(degrees) north of west). Thanks for any help.

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Doc Al
Mentor
Find the magnitude and direction of vector C.
What's vector C?

C=A-B (the displacement from plane 2 to plane 1)

Doc Al
Mentor
C=A-B (the displacement from plane 2 to plane 1)
Good. So what are the components of A and B? (Call East +x, and North +y)

Good. So what are the components of A and B? (Call East +x, and North +y)
Ax= (-220km)cos32
Ay= (220km)sin32
Bx= (140km)cos65
By=(140km)sin65

Doc Al
Mentor
Ax= (-220km)cos32
Ay= (220km)sin32
OK.
Bx= (140km)cos65
By=(140km)sin65
Careful: The angle here is given with respect to the North (y), not the East (x).

Careful: The angle here is given with respect to the North (y), not the East (x).
Ahh yes, thank you! I have found the solution.