https://login.i-ready.com/student/dashboard/home
13
30
Given that a vector is the directed line segment from P(0, 0) to Q(3,2), what is the magnitude of
that vector?
13
√13
√5
Done ->



Answer :

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.