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Find the distance of the plane 2x 3y + ...

Find the distance of the plane `2x 3y + 4z 6 = 0`from the origin.

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To find the distance of the plane given by the equation \(2x - 3y + 4z + 6 = 0\) from the origin, we can use the formula for the distance \(D\) from a point to a plane. The formula is: \[ D = \frac{|Ax_0 + By_0 + Cz_0 + D|}{\sqrt{A^2 + B^2 + C^2}} \] Where: - \(A\), \(B\), and \(C\) are the coefficients of \(x\), \(y\), and \(z\) in the plane equation \(Ax + By + Cz + D = 0\). ...
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Knowledge Check

  • The distance of the plane 6x-3y+2z-14=0 from the origin is

    A
    2
    B
    1
    C
    14
    D
    8
  • If the perpendicular distance of the plane 2x+3y-z= k from the origin is sqrt(14) units then k=……..

    A
    14
    B
    196
    C
    ` 2 sqrt (14)`
    D
    ` (sqrt(14))/(2)`
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