**Problem 1B-01:** Position vectors originated from one reference point

Use the summation and subtraction of position vectors of the first kind as defined in Topic 1-7 to perform the following operations.

(a) Draw position vectors expressed in rectangular coordinates,

on x-y plane.A= (5, 3),B= (-1, 2),C= (0, -2),

(b) Draw **A** + **B** +3**C** on the same graph as (a).

(c) Position vector **D** originates from the origin, has a length of
3 and points exactly northwest. Draw it on the x-y plane.
Express **D** in rectangular coordinates.

(d) **E** and **F** both originate from the origin. **E**
points north-north-east, forming an angle of 60 degree with x-axis,
and the magnitude of **E**, |**E**|, is 3. **F** points
south-east-east, forming an angle of -30 degree with the x-axis, and
|**F**| = 4. Express both position vectors in rectangular
coordinates.

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**Solution:**

(a) The solutions are drawn in the following graph

(b) **A**+**B**+3**C** = (5+(-1)+3·(0), 3+2+3·(-2)) = (4, -1).

The position vector is shown in the following graph.

(c) The position vector **D** is shown in the figure. From the picture we get

(d) Position vectors **E** and **F** are drawn in the following picture.

In the rectangular coordinate representations, we get

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