What is the magnitude of the vector
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.