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AP EAMCET · Maths · Three Dimensional Geometry

If the equation of the plane passing through the point \((3,2,5)\) and perpendicular to the planes \(2 x-3 y+5 z=7\) and \(5 x+2 y-3 z=11\) is \(x+b y+c z+d=0\), then \(2 b+3 c+d=\)

  1. A \(0\)
  2. B \(35\)
  3. C \(1\)
  4. D \(20\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(35\)

Step-by-step Solution

Detailed explanation

\(\vec{n_1} = (2, -3, 5), \vec{n_2} = (5, 2, -3)\) \(\vec{n} = \vec{n_1} \times \vec{n_2} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & -3 & 5 \\ 5 & 2 & -3 \end{vmatrix} = \mathbf{i}(9-10) - \mathbf{j}(-6-25) + \mathbf{k}(4-(-15)) = (-1, 31, 19)\) Plane…