To find the component form of the vector PQ, we first need to determine the coordinates of points P and Q. Point P has coordinates (2, 9) and point Q has coordinates (4, 14).
The component form of a vector PQ can be expressed as:
PQ = Q – P
Calculating the components:
- For the x-component: 4 – 2 = 2
- For the y-component: 14 – 9 = 5
Thus, the component form of the vector PQ is:
PQ = (2, 5)
Next, we need to find the magnitude of the vector PQ. The magnitude (length) of a vector can be calculated using the formula:
|PQ| = √(x1² + y1²)
Substituting our components into the formula:
|PQ| = √(2² + 5²) = √(4 + 25) = √29
In conclusion, the component form of vector PQ is (2, 5) and its magnitude is √29.