Find the value of p if the lines, whose equations are 2x - y + 5 = 0 and px + 3y = 4 are perpendicular to each other.

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Solution

2x - y + 5 = 0

y = 2x + 5

Slope of this line = 2

px + 3y = 4

3y = -px + 4

y = $fraction numerator negative p over denominator 3 end fraction x plus 4 over 3$

Slope of this line = $fraction numerator negative p over denominator 3 end fraction$

Since, the lines are perpendicular to each other, the product of the slopes is -1.

$2 open parentheses fraction numerator negative p over denominator 3 end fraction close parentheses equals negative 1 fraction numerator 2 p over denominator 3 end fraction equals 1 p equals 3 over 2$

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