Question

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
√5
1
√13

Explanation:

Step1: Recall the magnitude formula

The magnitude of a vector from \( P(x_1,y_1) \) to \( Q(x_2,y_2) \) is given by \( \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Here, \( P(0,0) \) and \( Q(3,2) \), so \( x_1 = 0,y_1 = 0,x_2=3,y_2 = 2 \).

Step2: Substitute values into the formula

Substitute the values into the formula: \( \sqrt{(3 - 0)^2+(2 - 0)^2}=\sqrt{3^2 + 2^2}=\sqrt{9 + 4}=\sqrt{13} \).

Answer:

\(\sqrt{13}\)