# Unit Vectors with No Scalar

I have a question on an assignment that expects the I+J form of a vector but is only giving the direction(cardinal) or angle of the vector. See example below:

## Homework Statement

Unit vectors and are directed east and north, respectively. Calculate the unit vector (in terms of I and J) in the following directions.

(a) northeast
(b) 47° clockwise from the -y axis
(c) southwest

All answers demand an I + J response and I'm can't exactly figure out what it wants or where to even start without a scalar.

## Homework Equations

Finding the I+J components with an angle of direction can be determined by using trigonometric functions to solve for components of the resulting reference right triangle.

## The Attempt at a Solution

For the (a) problem, I tried putting in s for scale and tried a few different pseudo type answers but was not successful. e.g. rcos(45)i + rsin(45)j

Has anyone seen problems like this particular one or have any ideas on what it's asking for?

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You are correct with the equation for part a with rcos(45)i+rsin(45)j defining the vector. All you need here to solve for the i and j components of the vector is r. r is the magnitude of the vector and in this case its a unit vector. Use the same approach for parts b and c.

So with it being a unit vector, r is = 1. This leaves me with the basic cos(45) & sin(45), etc... for their respective I+J values. I should be able to find the other solutions with trig functions as well.

Awesome! Thanks for giving me a push in the right direction!

You have been given that i and j are directed to the east and north. This follows the standard convention for a 2D Cartesian coordinate system in which i and j are directed along the positive x and y axis respectively.

In this system, a unit vector with a direction alpha, measured counterclockwise from the x axis, is:

(Cos[alpha],Sin[alpha])

or in terms of i and j:

Cos[alpha] i + Sin[alpha] j

The angles (in degrees) you have been given are 135, 47, and 225