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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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Knowledge Check

  • Equation of the line passing through hati+hatj-3hatk and perpendicular to the plane 2x-4y+3z+5=0 is

    A
    `(x-1)/2=(1-y)/(-4) =(z-3)/3`
    B
    `(x-1)/2=(1-y)/4=(z+3)/3`
    C
    `(x-2)/1=(y+4)/1=(z-3)/3`
    D
    `(x-1)/(-2) =(1-y)/(-4)=(z-3)/3`

  • The staight line passing through the point (1,0,-2) and perpendicular to the plane x-2y+5z-7=0 is

    A
    `(x-1)/1=y/0=(z-5)/(-2)`
    B
    `(x-1)/5=y/(-2)=(z+2)/1`
    C
    `(x-5)/(-2) =(y-1)/(-5) =z/1`
    D
    `(x-1)/1=y/(-2) =(z+2)/5`

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