# Chapter 7 - Test - Page 416: 29

$b=-\frac{5}{3}$

#### 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: $b=-\frac{5}{3}$.

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