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Question

Which of the following planes are parallel but not identical?
P1:4x2y+6z=3
P2:4x2y2z=6
P3:6x+3y9z=5
P4:2xyz=3

A
P2 & P3
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B
P2 & P4
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C
P1 & P3
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D
P1 & P4
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Solution

The correct option is B P1 & P3
a) for P2 & P3
Since, a1a2=b1b2c1c2d1d2
Therefore, planes are not parallel
b) for P2 & P4
Since, a1a2=b1b2=c1c2=d1d2
Therefore, planes are identical
c) for P1 & P3
Since, a1a2=b1b2=c1c2d1d2
Therefore, planes are parallel and identical
d) for P1 & P4
Since, a1a2b1b2c1c2d1d2
Therefore, planes are not parallel
Ans: C

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