How do you find the component form and magnitude of the vector from point P (2, 9) to point Q (4, 14)?

To find the component form and magnitude of the vector
PQ, which goes from point P to point Q, we can follow these steps:

Determine the coordinates:
Point P has the coordinates (2, 9) and point Q has the coordinates (4, 14).
Calculate the components of the vector:
The components of the vector
PQ can be found by subtracting the coordinates of point P from the coordinates of point Q.
```
PQ = Q - P = (4 - 2, 14 - 9) = (2, 5)
```
So, the component form of the vector
PQ is (2, 5).
Calculate the magnitude of the vector:
The magnitude of a vector can be calculated using the formula:
```
|PQ| = √(x² + y²)
```
In our case, x = 2 and y = 5:
```
|PQ| = √(2² + 5²) = √(4 + 25) = √29
```
Thus, the magnitude of |
PQ| is √29.

In summary: