# The two lines $\dpi{100} x=ay+b,z=cy+d\;$ and $\dpi{100} x=a'y+b',z=c'y+d'\;$ are perpendicular to each other if Option 1) $aa'+cc'=-1\;$ Option 2) $\; aa'+cc'=1\;$ Option 3) $\; \frac{a}{a'}+\frac{c}{c'}=-1\;$ Option 4) $\; \frac{a}{a'}+\frac{c}{c'}=1$

V Vakul

As we learnt in

Condition for perpendicularity -

$\vec{n}.\vec{n_{1}}= 0$ or $a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}=0$

-

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

$L_{2}:\frac{{x-b}'}{{a}'}=\frac{y}{-1}=\frac{{z-d}'}{{c}'}$

${aa}'+1+{cc}'= 0$

Option 1)

$aa'+cc'=-1\;$

Incorrect Option

Option 2)

$\; aa'+cc'=1\;$

Correct Option

Option 3)

$\; \frac{a}{a'}+\frac{c}{c'}=-1\;$

Incorrect Option

Option 4)

$\; \frac{a}{a'}+\frac{c}{c'}=1$

Incorrect Option

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