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The condition that the straight lines $x = a_{1} y + b_{1}; z = c_{1} y + d_{1}$ and $x = a_{2} y + b_{2}; z = c_{2} y + d_{2}$ are perpendicular, is

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a1a2+c1c2=1

a1a2+c1c2=-1

a1a2+c1c2=2

a1a2+c1c2=0

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detailed solution

Correct option is B

The given lines rewrite in symmetric form as x−b1a1=y=z−d1c1 and x−b2a2=y=z−d2c2The above two lines are perpendicular, hence a1a2+1+c1c2=0

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The condition that the straight lines x=a1y+b1; z=c1y+d1and x=a2y+b2; z=c2y+d2 are perpendicular, is

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The condition that the straight lines $x = a_{1} y + b_{1}; z = c_{1} y + d_{1}$ and $x = a_{2} y + b_{2}; z = c_{2} y + d_{2}$ are perpendicular, is