## Trigonometry 7th Edition

$a=-8$
Step 1: Since vectors $a\textbf {i}+6\textbf {j}$ and $9\textbf {i}+12\textbf {j}$ are perpendicular, their dot product must be zero. $(a,6)\cdot(9,12)=a(9)+6(12)=9a+72=0$. Step 2: Now, to find $b$, we must solve the above equation. Step 3: $9a+72=0$ Step 4: Subtract 72 from both sides: $9a+72-72=0-72$. Step 5: $9a=-72$ Step 6: Dividing both sides by $9$, $\frac{9a}{9}=\frac{-72}{9}$ Step 7: Simplifying, $a=-8$.