Vector Total Displacement Question?

Draw a diagram (xy axes) and mark the given points A, B and C.

Draw an arrow from the start point A(42, 48) to the end point C(11,12). This arrow is the displacement. Where point B is doesn't matter.

From Pythagoras:

|AC|² = (42-11)² + (28-12)²

. . . . .= 31² + 16²

. . . . = 1217

|AC| =√1217

. . . . = 34.9m (that's the magnitude)

If you imagine a new set of xy axes drawn so the origin is the start point point (A), the direction of AC is into the 3rd quadrant.

AC is an angle θ anticlockwise from the new -x axis where

tanθ = 16/31 = 0.5161

θ = tan⁻¹0.5161 = 27°

So, measured clockwise from the +x axis, the direction is 180° + 27° = 207° (which is the usual way to give the direction).

Adding 2 vectors this way is an essential skill for many problems. Try the video in the link.