Respuesta :
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]
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]
Answer: The magnitude of the vector u is √12 units.
Step-by-step explanation: Given that the dot product of a vector u with itself is 12.
We are to find the magnitude of the vector u.
Let <a, b> represents the vector u.
That is, u = <a, b>
Then, according to the given information, we have
[tex]u.u=12\\\\\Rightarrow <a, b>.<a, b>=12\\\\\Rightarrow a^2+b^2=12\\\\\Rightarrow \sqrt{a^2+b^2}=\sqrt{12}\\\\\Rightarrow |u|=\sqrt{12}.[/tex]
Thus, the magnitude of the vector u is √12 units.
