Answer
$b=-\frac{5}{3}$
Work Step by Step
Step 1: Since vectors $5\textbf {i}+12\textbf {j}$ and $4\textbf {i}+b\textbf {j}$ are perpendicular, their dot product must be zero.
$(5,12)\cdot(4,b)=5(4)+12(b)=20+12b=0$.
Step 2: Now, to find $b$, we must solve the above equation.
Step 3: $20+12b=0$
Step 4: Subtracting 20 from both sides, $20+12b-20=0-20$
Step 5: $12b=-20$
Step 6: Divide both sides by $12$: $\frac{12b}{12}=\frac{-20}{12}$.
Step 7: Simplify: $b=-\frac{5}{3}$.
