# Thread: Require assistance with this vectors question. #1

1. ## Require assistance with this vectors question. #1

Extremely difficult for me, just started learning about vectors, need a worked solution.
Problem is in the image attached.

2. ## Re: Require assistance with this vectors question. #1

Originally Posted by kel0021

Extremely difficult for me, just started learning about vectors, need a worked solution.
Problem is in the image attached.
Use your index finger to do those exercises:

1. Go from A to C: From A to B + from B to C. With vectors:

$\displaystyle \overrightarrow{AC} = \vec a + \vec b$

Since P is the midpoint of AC you'll get:

$\displaystyle \overrightarrow{AP} = \frac12 (\vec a + \vec b)$

2. According the method from #1 you'll get

$\displaystyle \overrightarrow{AQ} = \vec a + \frac12 \cdot \vec b$

3. You "go" from P to Q like: From P to A + from A to Q. With vectors:

$\displaystyle \overrightarrow{PQ} = -\frac12 \cdot ( \vec a + \vec b) + \vec a + \frac12 \cdot \vec b$

$\displaystyle \overrightarrow{PQ} = \frac12 \cdot \vec a$

4. This vector has the same direction as $\displaystyle \vec a$ and half of it's length.