Answer
46
Work Step by Step
$(\vec{a}+\vec{b})=(a_{x}+b_{x})\hat{i}+(a_{y}+b_{y})\hat{j}+(a_{z}+b_{z})\hat{k}$
$=(3.0+2.0)\hat{i}+(5.0+4.0)\hat{j}=5.0\hat{i}+9.0\hat{j}$
Multiplying the coefficients of $\hat{i},\,\hat{j}$ and $\hat{k}$ of the vector $(\vec{a}+\vec{b})$ with the corresponding coefficients of $\vec{b}$, we get
$(\vec{a}+\vec{b})\cdot\vec{b}=(5.0\times2.0)+(9.0\times4.0)=46$
