# Vector and components problem

A radar station, located at the origin of xz plane, as shown in the figure, detects an airplane coming straight at the station from the east. At first observation (point A), the position of the airplane relative to the origin is R_vec_A. The position vector R_vec_A has a magnitude of 360m and is located at exactly 40 degrees above the horizon. The airplane is tracked for another 123 degrees in the vertical east-west plane for 5.0s, until it has passed directly over the station and reached point B. The position of point B relative to the origin is R_vec_B (the magnitude of R_vec_B is 880 m).
I'm suppose to find the ordered pair (x,z) for components of the vector R(AB), which I am suppose to be able to find by R(AB) = R(B) - R(A).

http://server6.theimagehosting.com/image.php?img=phytest.jpg

So far, I solved for the components of the vector of B, and the vector of A.

Vector A:
cos 40 = x/360; x = 276
sin 40 degrees = y/360; y = 231
= (276, 231)

Vector B:
I guess to use sin, cos, tan I need a right angle. So I do the bottom of B to do it. (123+40=163; 180-163=17 degrees)
cos 17 = x/880; x = 842
sin 17 = y/880; y = 257
= (842, 257)

Vector B - Vector A = (842, 257) - (276, 231) = (566, 26)

Which is wrong. What am I doing wrong? Should I be doing Vector B a different way? Or did I do the entire thing wrong?

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Kurdt
Staff Emeritus
Gold Member
What you've forgotten to do is to take into account that the B x coordinate should be negative because you have crossed the perpendicular to the origin.

B = (-842,257)

easy mistake to make.

Well, that makes it:
(-842, 257) - (276, 231) = (-1118, 26)

Unfortunately it's still wrong, I guess I'll have to think of something else.

Kurdt
Staff Emeritus