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?

Answer 1

To find the magnitude of the vector \(\vec{PQ}\) from point \(P(0,0)\) to point \(Q(3,2)\), we can use the formula for the magnitude of a vector \(\vec{v} = (x, y)\), given by:

\[
|\vec{v}| = \sqrt{x^2 + y^2}
\]

In this case, the vector \(\vec{PQ}\) can be defined as:

\[
\vec{PQ} = Q - P = (3 - 0, 2 - 0) = (3, 2)
\]

Now, we can calculate the magnitude:

\[
|\vec{PQ}| = \sqrt{3^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}
\]

Thus, the magnitude of the vector is:

\[
\sqrt{13}
\]