A vector with magnitude 2km and a direction of Southwest, what are its components in terms of N and E?

Question

If I have a vector with magnitude 2km and a direction of Southwest, what are its components in terms of North and East?

Please explain

Answer 1

If the vector is SW, the N and E components would both be negative. If it is true SW (equally South AND West), it's sqrt(2)*2kM (square root of 2 because of the 45deg angle) for both Northing and Easting

Answer 2

You can use sine and cosine to find the components if you don't know about 45º-45º-90 right triangles:
∆D = 2 km
ө = 45º (southwest is 45º from the horizontal)
sin Ó© = opp/hyp
sin ө = ∆Dx/∆D
∆Dx = ∆D sin ө
∆Dx = (2 km) (sin 45º)
∆Dx = (2 km) (0.7071067811865475244)
∆Dx = 1.41421356237309504880 km
And since it is a 45º angle, the 2 legs of the triangle are equal, so ∆Dx is equal to ∆Dy.
∆Dy = 1.41421356237309504880 km
However, this is the change in distance to the south and to the west. Since north and east are opposites of south and west, simply reverse the sign:
∆Dx = -1.41421356237309504880 km
∆Dy = -1.41421356237309504880 km