**Problem 1B-02:** Position vectors, geometric approach

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

(a) Position vectors **A** and **B** are given in the following picture.
Draw **A**+**B**.

(b) Position Vectors **C** and **D** are given in the following
picture. Draw **C**-**D**.

(c) Position vectors **A**, **B** and **C** are given in the
picture. Draw **A**+**B**-**C**. Does **A**-**C**+**B**
has any physical meaning?

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**Solution:**

The solutions here are based on the summation and subtraction of
position vectors of the first kind as defined in Topic 1-7.

(a) The answerer is shown as red position vector that originates from the origin and
specify point P in the following picture.

The procedure is to draw a parallelogram with **A** and **B** as two
adjacent sides. Other two sides of the parallelogram are shown as blue lines
in the above picture. The diagonal OP then is the desired answer
**A**+**B**.
(b)

Form a parallelogram with **D** as one side and **C** as a diagonal
as shown in the above picture. The the other side originating from the
origin 0 and ending at point P is the desired answer **C**-**D**.
(c)

In the above picture first draw a parallelogram with **A** and **B**
as two adjacent sides; other two sides of the parallelogram are shown as
blue lines. The diagonal of the parallelogram originating from the origin is
the sum **A**+**B**. Then form a parallelogram with **C** as one
side and **A**+**B** as a diagonal; the other two sides of the
parallelogram are colored in orange. The remaining side, colored in red is
the answer **A**+**B**-**C**. To form the vector
**A**-**C**+**B** we use the following picture.

We first draw a parallelogram with **A** as a diagonal and **C** as
one side; other two sides are colored orange. The fourth side colored blue
is the position vector **A**-**C**. The parallelogram with
**A**-**C** and **B** as two sides are drawn with other two sides
colored blue. The diagonal of this last parallelogram, colored red, is the
position vector **A**-**C**+**B**. Please note that the result of
**A**-**C**+**B** constructed here is the same as
**A**+**B**-**C** that is constructed in conjunction with the
previous graph.