Vector displacement equation trouble

[Melchior25]

Homework Statement

A radar station locates a ship in distress at horizontal range 16.0 km and bearing 136° clockwise from north. From the same station a rescue plane is at horizontal range 19.6 km, 148° clockwise from north, with elevation 1.80 km.

(a) Write the vector displacement from plane to ship, letting i represent east, j north, and k up.

Homework Equations

Vector Displacement - A=A(x)i+A(y)j+A(z)k

I also converted the polar coordinates to Cartesian coordinates.

x=r*cos(theta)
y=r*sin(theta)

x1 = -11.5094
y1 = -11.1145

x2 = -16.6217
y2 = -10.3864

The Attempt at a Solution

So far this is what I have...

vector displacement = (-11.5094 + -16.6217)i + (-11.1145 + -10.3864)j + (1.80)k

I have a feeling though that I am not doing something right. Could someone please double check. Thanks

 

[Melchior25]

Note: Every time I put the answers in I get the response that I used the wrong sign.

 

[neutrino]

Given two points P₁ and P₂, the vector displacement from P₁ to P₂ is v₂-v₁. (the v's are the position vectors of the points.)

 

[HallsofIvy]

Homework Statement

A radar station locates a ship in distress at horizontal range 16.0 km and bearing 136° clockwise from north. From the same station a rescue plane is at horizontal range 19.6 km, 148° clockwise from north, with elevation 1.80 km.

(a) Write the vector displacement from plane to ship, letting i represent east, j north, and k up.

Homework Equations

Vector Displacement - A=A(x)i+A(y)j+A(z)k

I also converted the polar coordinates to Cartesian coordinates.

x=r*cos(theta)
y=r*sin(theta)

x1 = -11.5094
y1 = -11.1145

x2 = -16.6217
y2 = -10.3864

The Attempt at a Solution

So far this is what I have...

vector displacement = (-11.5094 + -16.6217)i + (-11.1145 + -10.3864)j + (1.80)k

I have a feeling though that I am not doing something right. Could someone please double check. Thanks

Did you draw a picture? The vector components from the station to the ship and from the station to the plane are exactly as you say. If you let "P" be the vector from the station to the plane, "S" the vector from the station to the ship, and "x" the vector from the plane to the ship, you should see that if you go from the station to the plane, then from the plane to the ship, that is the same as going directly from the station to the ship. In other words, S+ x= P. Then x= P- S. You want to subtract the vectors you calculated, not add them!

 

[Melchior25]

Of course, I did draw the picture. Every time I have a physics problem. I see what you're saying and it had not slipped my mind. Right after the post I did notice that I added them and then subtracted them but unfortunately I still get the wrong answer. Now I'm just stumped.