If $\text{A}=6.00\hat{i}-8.00\hat{j}\text{units,}$ $\text{B}=8.00\hat{i}+3.00\hat{j}\text{units}$ and $\text{C}=26.0i-19.0j\text{units}$ , determine a and b when a $\text{A}+\text{bB}+\text{C}=0$

$\overrightarrow{B}=8\hat{i}+3\hat{j}$

$\overrightarrow{C}=26\hat{i}-19\hat{j}$

$\text{given}\text{a}\overrightarrow{A}+\text{b}\overrightarrow{B}+\overrightarrow{C}=\overrightarrow{0}$

$6\text{a}+8\text{b}=-26\times \left(8\right)$

$\underset{\_}{-8\text{a}+\text{3b}=-19\times \left(6\right)}$

$48\text{a}+64\text{b}=-208$

$\underset{\_}{-48\text{a}+18\text{b}=-114}$

$82\text{b}=-322$

$\text{b}=\frac{-322}{82}=-3.92$

$\text{a}=0.9$