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Equation of the passing through the orig...

Equation of the passing through the origin and perpendicular to the planes `x+2y+z=1`, `3x-4y+z=5` is

A

`x+2y-5z=0`

B

`x-2y-3z=0`

C

`x-2y+5z=0`

D

`3x+y-5z=0`

Text Solution

Verified by Experts

The correct Answer is:
D
Required plane is perpendicular to the line of intersection of given two planes.
vector along the line of intresection of planet is
`|{:(hati,hatj,hatk),(1,2,1),(3,-4,1):}|=6hati+2hatj-10hatk`
`therefore` Required plane is `3x+y-5z=0`
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