If north is the direction of the positive y-axis and east is the direction of the positive x-axis, give the unit vector pointing northwest.

North is the direction of positive y-axis. East is the direction of positive x-axis. So West will be the direction of negative x-axis.

Northwest will mean, in between north and west i.e. in between y-axis and the negative x-axis which is the mid of the 2nd quadrant. Thus the vector pointing northwest will form an angle of 135 degrees with positive x-axis.

The magnitude of unit vector is 1 and is forming an angle of 135 degrees. In terms of its components, we can write:

x-component = 1 cos (135) = 
y-component = 1 sin (135) =

Thus the unit vector will be = 

In vector form, component form the vector can be written as:

A vector pointing northwest passes through point (-1, 1).

Thus an example of a unit vector pointing northwest is .

Recall that a vector is made a unit vector by dividing each component of the vector by the magnitude of the vector.

The magnitude of vector  is given by .

Thus, a unit vector pointing northwest is  which when we rationalize we have .