The two lines x= {\ay}+ {\b}, {\z}= {\cy}+ {\d}; and x= ...

CBSE Class 12 Math 2020 Outside Delhi Set 1 Solved Paper

Question : 6 of 36

Marks: +1, -0

The two lines

x= {\ay}+ {\b}, {\z}= {\cy}+ {\d}

; and

x= {\a}^{'} {\y}+ {\b}^{'}, {\z}= {\c}^{'} {\y}+ {\d}^{'}

are perpendicular to each other, if

Solution: 👈: Video Solution

Fact: Two lines

\;{x-x_1}/{a_1}=\;{x-y_1}/{b_1}=\;{z-z_1}/{c_1}

and

\;{x-x_2}/{a_2}=\;{y-y_2}/{b_2}=\;{z-z_2}/{c_2}

are

⟂

a_1 a_2+b_1 b_2+c_1 c_2=0

Given lines can be written as

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

(i)
and

\;{x-b^{'}}/{a^{'}}=\;{y}/{1}=\;{z-d^{'}}/{c^{'}}

As lines are perpendicular

∴ \;\; a a^{'}+1+c c^{'}=0

⇒ \;\; a a^{'}+c c^{'}=-1

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