Question Video: The Magnitude of a Vector Mathematics

Video Transcript

What is the magnitude of the vector five, 12?

We know that for any vector written in the form 𝑎, 𝑏, the magnitude is equal to the square root of 𝑎 squared plus 𝑏 squared. As the magnitude is the length of the vector, this can be shown on a grid. Let’s consider the vector 𝐯 as shown. If this vector has moved a distance 𝑎 in the horizontal direction and 𝑏 in the vertical direction, we can create a right triangle. Using Pythagoras’s theorem, the square of the hypotenuse is equal to 𝑎 squared plus 𝑏 squared. This means that the length of the vector will be equal to the square root of 𝑎 squared plus 𝑏 squared.

In this question, the two components of the vector are five and 12. We can therefore calculate its magnitude by finding the square root of five squared plus 12 squared. Five squared is equal to 25, and 12 squared is equal to 144. This means that the magnitude of vector 𝐯 is the square root of 169. As our answer must be positive, the magnitude of vector 𝐯 is 13.