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If the distance between the plane ax 2y...

If the distance between the plane ax 2y + z = d and the plane containing the lines `(x-1)/2=(y-2)/3=(z-3)/4` and `(x-2)/3=(y-3)/4=(z-4)/5` is `sqrt6` , then value of |d| is

Text Solution

Verified by Experts

The correct Answer is:
`6`
Let normal to plane be `lhati+mhatj+nhatk`
`" "2l+3m+4n=0`
and `" "3l+4m+5n =0`
`" "(l)/(-1) = (m)/(2)= (n)/(-1)`
Equation of plane will be
`" "a(x-1)+b (y-2)+c(z-3)=0`
or `" "-1(x-1)+2(y-2)-1(z-3)=0`
or `" "-x+1+2y-4-z+3=0`
or `" "-x+2y+z=0`
or `" "x-2y+z=0`
or `" "(|d|)/(sqrt6) = sqrt6`
or `" "d=6`
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Knowledge Check

  • The angle between the lines (x+1)/(3)=(y-2)/(-2)=(z+4)/(1) and (x-3)/(1) =(2y-3)/(5)=(z-2)/(2) is -

    A
    `(pi)/(3)`
    B
    `(pi)/(2)`
    C
    `"cos"^(-1)(3)/(5)`
    D
    `"cos"^(-1)(4)/(5)`

  • The lines (x)/(1)=(y)/(2)=(z)/(3) and (x-1)/(-2)=(y-2)/(-4)=(3-z)/(6) are

    A
    coincident
    B
    skew
    C
    intersecting
    D
    parallel

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