CBSE Class 12 Math 2020 Outside Delhi Set 1 Solved Paper

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Question : 6
Total: 36
The two lines x=ay+b,z=cy+d; and x=a′y+b′,z=c′y+d′ are perpendicular to each other, if
Fact: Two lines ‌
x−x1
a1
=‌
x−y1
b1
=‌
z−z1
c1

and ‌
x−x2
a2
=‌
y−y2
b2
=‌
z−z2
c2

are ⟂ if a1a2+b1b2+c1c2=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
∴‌‌aa′+1+cc′=0
⇒‌‌aa′+cc′=−1
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