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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.

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

Thus an example of a unit vector pointing northwest is
-i+j.

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
-i+j is given by
|-i+j|=√((-1)^2+1^2)=√(1+1)}=√(2).

Thus, a unit vector pointing northwest is
- (1)/(√(2)) i+ (1)/(√(2)) j which when we rationalize we have
- (√(2))/(2) i+ (√(2))/(2) j.
User Alexey Timokhin
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5 votes
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) =
- ( √(2) )/(2)
y-component = 1 sin (135) =
( √(2) )/(2)

Thus the unit vector will be =
- ( √(2) )/(2)x+ ( √(2) )/(2)y

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


(- ( √(2) )/(2), ( √(2) )/(2))
User Dkozl
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8.9k points

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