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Question
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
Options
aa′ + bb′ = 0
ab′ = ba′
ab + a′b′ = 0
ab′ + ba′ = 0
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Solution
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if aa′ + bb′ = 0
Explanation:
Slope of the line ax + by = c is `(-a)/b`.
And the slope of the line a′x + b′y = c′ is `(-a"'")/(b"'")`.
The lines are perpendicular if tan θ = `3/(5 - x)`
`(-a)/b (-a"'")/(b"'")` = − 1 or aa' bb′ + = 0 (Why?)
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