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Question

The line x-23=y-34=z-45is parallel to the plane


A

3x+4y+5z=7

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B

2x+3y+4z=0

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C

x+y-z=2

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D

2x+y-2z=0

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Solution

The correct option is D

2x+y-2z=0


Explanation for the correct option:

Given: line x-23=y-34=z-45

let x-23=y-34=z-45=λ

3i^+4j^+5k^=a will be perpendicular to normal vector of a plane.

Checking option D

So,

=3(2)+4(1)+5(-2)=6+4-10=0

Hence, 2x+y-2z=0 is parallel to x-23=y-34=z-45.

Explanation for the in-correct options:

Option A 3x+4y+5z=7

3i^+4j^+5k^=a and normal vecotor to the plane is 3i^+4j^+5k^=n

Both vector are parallel so option (A) is incorrect.

Option(B) 2x+3y+4z=0

2i^+3j^+4k^=n and 3i^+4j^+5k^=a

a.n=6+12+200

So, option B is also incorrect.

Option(C) x+y-z=2

i^+j^-k^=n and 3i^+4j^+5k^=a

a.n=3+4-50

So, option C is also incorrect.

Hence,option D is correct.


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