Q86 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Mathematics

The distance of the plane \(2 x-y-2 z-9=0\) from the origin is units.

  • Correct answer
    A
    3
  • B
    \(\sqrt{3}\)
  • C
    1
  • D
    9

Solution

Distance of plane \(A x+B y+C z+d=0\) from \(\left(x_1 y_1 z_1\right)\) is given by \(d=\left|\frac{A x_1+B y_1+C z_1+D}{\sqrt{A^2+B^2+C^2}}\right|\) By comparision, substituting values \(d=\left|\frac{2 \times 0+(-1)(0)+(-2)(0)-9}{\sqrt{2^2+(-1)^2+(-2)^2}}\right|=\left|\frac{-9}{\sqrt{9}}\right|=3 \text { units. }\)

Hence, the correct answer is option: 'A'.

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