# Vector airplane distance problem

## Homework Statement

An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 900 m, horizontal distance 19.0 km, and 25.0° south of west. The second aircraft is at altitude 1200 m, horizontal distance 17.6 km, and 17.0° south of west. What is the distance between the two aircraft? (Place the x axis west, the y axis south, and the z axis vertical.)

## The Attempt at a Solution

my vectors for each airplane are:

<17.22, 8.03, .9>
<16.83, 13.18, 2.1>

adding them together and then getting the resultant i get 36.57 kilometers, however thats wrong and i'm not sure what i did wrong.

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cepheid
Staff Emeritus
Gold Member
For your second vector, neither the y-component nor the z-component is correct.

cepheid
Staff Emeritus
Gold Member
Also, adding them together and taking the resultant is not what you want to do. Think about it. Draw a picture.

For your second vector, neither the y-component nor the z-component is correct.
sorry that was a typo...i accidently wrote down the added values.

Also, adding them together and taking the resultant is not what you want to do. Think about it. Draw a picture.
ahh i see, i believe i should have subtracted the vectors?

reworking the problem by subtracting, i get 2.96 km...could someone verify my answer?

cepheid
Staff Emeritus
Gold Member
Subtracting is the right thing to do to find a vector that goes from one plane to the other. Then you need to find the magnitude of this vector.

I get an answer that is pretty close to that.

Subtracting is the right thing to do to find a vector that goes from one plane to the other. Then you need to find the magnitude of this vector.

I get an answer that is pretty close to that.
ok yes that is what i did for my second answer...thank you for the help!