Respuesta :

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) = [tex]- \frac{ \sqrt{2} }{2} [/tex]
y-component = 1 sin (135) = [tex]\frac{ \sqrt{2} }{2} [/tex]

Thus the unit vector will be = [tex]- \frac{ \sqrt{2} }{2}x+ \frac{ \sqrt{2} }{2}y[/tex]

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

[tex](- \frac{ \sqrt{2} }{2}, \frac{ \sqrt{2} }{2}) [/tex]
nobillionaireNobley
A vector pointing northwest passes through point (-1, 1).

Thus an example of a unit vector pointing northwest is [tex]-i+j[/tex].

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 [tex]-i+j[/tex] is given by [tex]|-i+j|=\sqrt{(-1)^2+1^2}=\sqrt{1+1}}=\sqrt{2}[/tex].

Thus, a unit vector pointing northwest is [tex]- \frac{1}{\sqrt{2}} i+ \frac{1}{\sqrt{2}} j[/tex] which when we rationalize we have [tex]- \frac{\sqrt{2}}{2} i+ \frac{\sqrt{2}}{2} j[/tex].

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