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Assuming your talking about simple math of vectors, each vector is made up of components in different directions and magnitudes.

Vector=V=ui+vj+wk

Where i is the unit vector in the x direction, v is in the y direction, and k is in the z direction. u,v,w are the components each of these directions.

If North is in the y direction and East is in the x direction, then a person traveling at 50 mi/h in the Northeast direction would have a Velocity in both i and j direction

V=ui+vj

Where 50mi/h=25*sqrt(25)i+25*sqrt(25)j

V=sqrt{[25*sqrt(25)i]^2+[25*sqrt(25)j]^2}=50

All of this said, you simply add the components of the two vectors together, i's plus i's and j's plus j's.

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