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Question
Find the value of p if the lines, whose equations are 2x – y + 5 = 0 and px + 3y = 4 are perpendicular to each other.
Solution
2x − y + 5 = 0
y = 2x + 5
Slope of this line = 2
px + 3y = 4
3y = − px + 4
`y = (-px)/3+ 4/3`
Slope of this line = `(-p)/3`
Since, the lines are perpendicular to each other, the product of the slopes is −1.
∴ `(2)((-p)/3)= -1`
`(2p)/3 = 1`
`p = 3/2`
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