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Consider the planes 3x-6y-2z=15a n d2x+y...

Consider the planes `3x-6y-2z=15a n d2x+y-2z=5.` Statement 1:The parametric equations of the line intersection of the given planes are `x=3+14 t ,y=2t ,z=15 tdot` Statement 2: The vector `14 hat i+2 hat j+15 hat k` is parallel to the line of intersection of the given planes.

A

Statement I is true, Statement II is also true,
Statement II is the correct explanation of
Statement I

B

Statement I is true, Statement II is also true,
Statement II is not the correct explanation of
Statement I

C

Statement I is true, Statement II is false

D

Statement I is false, Statement II is true

Text Solution

Verified by Experts

The correct Answer is:
D
Given planes are `3x-6y-2z=15` and `2x+y-2z=5.`
For z=0, we get x=3, y=-1
Since, direction ratios of planes are
`lt3,-6,-2gt" and "lt2,1,-2gt`
Then the DR's of line of intersection of planes is `lt14,2,15gt` and line is
`(x-3)/(14)=(y+1)/(2)=(z-0)/(15)=lambda" "["say"]`
`implies" "s=14lambda+3,y=2lambda-1,z=15lambda`
Hence, Statement I is false.
But Statement II is true.
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