What is the dot product of a vector with itself?
If I have a vector A and I dot it with itself, then according
to our definition it would be A x squared plus A y squared
plus A z squared.
Now keep in mind that the magnitude of A itself is the
square root of Ax squared plus Ay squared plus Az squared.
So this is nothing but the magnitude of A squared.
So if we take our famous vector A, which was 3 x roof
minus 2 y roof plus 4 z roof, then the magnitude of that
vector equals the square root of 29.
But A dot A, which is a scalar.
And you can check that easily by applying this rule.
You will see that that is 29, which is exactly the square of
the magnitude of A.