Answer: [tex] \sqrt{65} [/tex] ≈ 8.06
Explanation:
The notation u = <4,7> means that the coordinates of the vector are 4 and 7.
The magnitude of a vector <a,b> is:
[tex]magnitude= \sqrt{a^2+b^2} [/tex]
So, for the magnitude of vector u is:
[tex]magnitude= \sqrt{4^2+7^2} = \sqrt{16+49}= \sqrt{65} [/tex]
Which if you want to approximate to a decimal number is ≈ 8.06.
The important thing is that you know the notation and what magnitude means.
As said, the notation used is to indicate the coordinates of the vector, which is the coordinates of the extreme of the vector, and the magnitude is the length of the vector. So, the formula of the magnitude is just the application of Pythagorean theorem:
[tex]hypotenuse^2=a^2+b^2[/tex]
