Determine the Length of the Crankshaft AB by first formulating a Cartesian position vector from A to B and then determining its magnitude.

#### Solution:

### Let us first write the Cartesian position vector from A to B like so:

### r_{AB}=((400\,+\,125\text{sin}(25^0))i\,-\,125\text{cos}(25^0)j)

##### (Here, we wrote the components of the x-axis and y-axis separately)

### Simplifying the terms inside the brackets gives us:

### r_{AB}=\left\{452.83i\,-\,113.3j\right\} mm