**Problem statement:**

Given the vectors: **A** = 3**i** + 2**j** – **k** and **B** = 5**i** +5**j**.

Determine:

- Their magnitude.
- The direction of
**B**. **A**+**B****A**-2**B**- A unit vector parallel to
**A**. - A vector of magnitude 2 and opposite to
**B**

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**Solution:**

It is essential when working with vectors to **use proper notation**. Always draw an arrow over the letters representing vectors. You can also use bold characters to represent a vector quantity.

Vectors **A** and **B** are written using the unit vector notation.

The magnitude of **A** is given by:

Similarly, the magnitude of **B** is:

**The magnitude of a vector is always a positive number**.

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In the figure below vector **B** is shown, as well as the standard unit vectors (in red).

As we saw when we first introduced the scalar and vector quantities, we can derive the polar components of a vector from the Cartesian coordinates:

The vector sum of

**A**and

**B**is given by:

In order to solve section (d) we multiply **B** by -2 and then we add **A**:

A unit vector is created from another one by dividing the last by its magnitude:

We can find a vector of magnitude 2 and opposite to **B** by multiplying a unit vector parallel to **B** by -2: