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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

  • The equation of a plane passing through origin and perpendicular to the line x=2y=3z is

    A
    x+2y+3z=0
    B
    3x+2y+z=0
    C
    6x+3y+2z=0
    D
    6x-3y+2z=0

  • The point of intersection of the plane 3x-5y+2z=6 with the straight line passing through the origin and perpendicular to the plane 2x-y-z=4 is

    A
    (1,-1,-1)
    B
    (-1,-1,2)
    C
    (4,2,2)
    D
    `(4/3,(-2)/3,(-2)/3)`

  • Equation of the line passing through (1,1,1) and perpendicular to the plane 2x+3y-z-5=0 is

    A
    `(x-1)/2=(y-1)/3 =(z-1)/1`
    B
    `(x-1)/2=(y-1)/3=(z-1)/-1`
    C
    `(x-1)/2=(y-1)/-1=(z-1)/1`
    D
    None of the above

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