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Question
The projection of the line x+1−1=y2=z−13 on the plane x – 2y + z = 6 is the line of intersection of this plane with the plane
The projection of the line x+1−1=y2=z−13 on the plane x – 2y + z = 6 is the line of intersection of this plane with the plane
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Solution
The correct option is A 2x + y + 2 = 0
Equation of plane through (–1, 0, 1) is
a(x + 1) + b(y – 0) + c(z – 1) = 0 . . . .(i)
Which is parallel to given line and perpendicular to given plane
– a + 2b + 3c = 0 . . . .(ii)
and a – 2b + c = 0 . . . .(iii)
From Eqs. (ii) and (iii), c = 0, a = 2b
From Eqs. (i), 2b(x + 1) + by = 0
⇒ 2x + y + 2 = 0
Equation of plane through (–1, 0, 1) is
a(x + 1) + b(y – 0) + c(z – 1) = 0 . . . .(i)
Which is parallel to given line and perpendicular to given plane
– a + 2b + 3c = 0 . . . .(ii)
and a – 2b + c = 0 . . . .(iii)
From Eqs. (ii) and (iii), c = 0, a = 2b
From Eqs. (i), 2b(x + 1) + by = 0
⇒ 2x + y + 2 = 0
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