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2 problems match “vector addition”. Clear

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1. Weighted inner product of a sum ●○○○○ 10 ptsLet $\langle u,v\rangle = 4u_1v_1 + 5u_2v_2$ for vectors $u=(u_1,u_2)$ and $v=(v_1,v_2)$ in $\mathbb{R}^2$. Given $u=(3,-2)$, $v=(4,5)$ and $w=(-1,6)$, find $\langle u+v, w\rangle$.
2. Side length from two dot products ●●●○○ 50 ptsIn $\triangle ABC$, $\overrightarrow{AB} \cdot \overrightarrow{AC} = \overrightarrow{AB} \cdot \overrightarrow{CB} = 4$. Find the length of side $AB$. Round to two decimal places.