QJEEM19Mafdeb: JEE Main 2019 Mathematics - Class 12 JEEM19Mafdeb Solution: If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + …

Question

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If the lines x = ay + b, z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then :

Accepted Answer

Equation of 1^st line is

\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}

Dr's of 1^st line = (

a

, 1 , c)

Equation of 2^nd line is

\frac{x - b^{'}}{a^{'}} = \frac{y - b^{'}}{c^{'}} = \frac{z}{1}

Dr's of 2^nd line = (

a^{'}

, c' , 1)

Lines are perpendicular, so the dot product of the Dr's of two lines are zero.

∴

a a

' + c + c' = 0

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