URGENT! Find Angle between between vectors using norms

View image: PROB

I don't understand how to use the information given. It's not like I can break up a sum inside a norm. I also don't know if this is in R^2 or R^3, so it's R^n

I know the formula:

cos theta = (u . v ) / ( ||u|| ||v|| )

and that norm squared is a vector dot itself

Re: URGENT! Find Angle between between vectors using norms

Quote:

Originally Posted by

**LightRay7** View image: PROB
I know the formula:

cos theta = (u . v ) / ( ||u|| ||v|| )

and that norm squared is a vector dot itself

All you need is th value of $\displaystyle \vec{a}\cdot\vec{b}$

$\displaystyle \begin{align*}100 &=\|\vec{a}+3\vec{b}\|^2\\ &= \vec{a}\cdot\vec{a}+9 \vec{b}\cdot\vec{b}+6\vec{a}\cdot\vec{b} \\ &=25+27+6 \vec{a}\cdot\vec{b}\\ 8&= \vec{a}\cdot \vec{b} \end{align*}$.