To find the magnitude of a vector from point P to point Q, we use the distance formula which is derived from the Pythagorean theorem. In two-dimensional space, if the coordinates of point P are (Px, Py) and the coordinates of point Q are (Qx, Qy), then the vector from P to Q has the components:
X component: Qx - Px
Y component: Qy - Py
The magnitude of the vector, also known as its length, is calculated by the distance formula:
Magnitude = √[(Qx - Px)² + (Qy - Py)²]
Given our points P(0, 0) and Q(3, 2), we can substitute the respective values:
Magnitude = √[(3 - 0)² + (2 - 0)²]
Magnitude = √[3² + 2²]
Magnitude = √[9 + 4]
Magnitude = √13
So, the magnitude of the vector from P(0, 0) to Q(3,2) is √13.
If you're referring to the multiple-choice options provided, the correct choice would be √13.
