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Question

Let a plane P1 containing the line L1:x−11=y−1−1=z−1−1 and P2 is another plane containing the line L1 and passes through point (0,1,1), if direction ratio of normal to the plane P1 is (1,1,0). then which of the following statement(s) is/are correct ?

A
The equation of plane P1 is : x+y=2
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B
The equation of plane P1 is : xy=2
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C
The equation of plane P2 is: xz=0
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D
The equation of plane P2 is: yz=0
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Solution

The correct option is D The equation of plane P2 is: yz=0
Given : line L1:x11=y11=z11 passes through (1,1,1),d.rs=(1,1,1)
Equation of plane P1 containing L1 and having normal d.rs=(1,1,0) is given by,
1(x1)+1(y1)+0=0x+y=2(i)
and equation of plane P2 containing L1 and passes through (0,1,1) is given by,
∣ ∣x1y1z1101111111∣ ∣=0
yz=0

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