The dot product of u with itself is 12. what is the magnitude of u?

let's say u = <a,b>.

we know it's dot product is 12, thus

[tex]\bf \ \textless \ a,b\ \textgreater \ \cdot \ \textless \ a,b\ \textgreater \ \implies (a\cdot a)+(b\cdot b)\implies \boxed{a^2+b^2=12}\\\\ -------------------------------\\\\ ||\ \textless \ a,b\ \textgreater \ ||=\sqrt{a^2+b^2}\implies \sqrt{\boxed{12}}[/tex]