
vector problem sum
A force F of 6 units acts in the direction 30 degrees west of north. An object is
constrained to move northwesterly, that is, 45 degrees west of north.
(a) Sketch the force vector roughly to scale on a set of axes that has the positive y
axis pointing north, and write F using exact values, either in the form (x; y) or
else in the form xi + yj.
(b) Write a vector in the direction of the given movement of the object.
(c) Without using trigonometric functions, ¯find both the scalar component and the
vector projection of F in the direction of movement of the object. Write both
answers as exact values, not decimal approximations.

It is hard to draw anything here.
You can use the fact that the cathete opposite to the angle is half the hypothenuse in length when the angle is 30 degrees.