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AP EAMCET · Maths · Three Dimensional Geometry

The distance of the point \(\mathrm{O}(\vec{O})\) from the plane \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=5\) measured parallel to \(2 \hat{i}+3 \hat{j}-6 \hat{k}\) is

  1. A \(35\)
  2. B \(30\)
  3. C \(25\)
  4. D \(4\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(35\)

Step-by-step Solution

Detailed explanation

Equation of plane: \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=5\) \(\Rightarrow x+y+z=5\) ....(i) A vector parallel to \(2 \hat{i}+3 \hat{j}-6 \hat{k}\) is \(2 \lambda \hat{i}+3 \lambda \hat{j}-6 \lambda \hat{k}\) \(\Rightarrow x=2 \lambda, y=3 \lambda, z=-6 \lambda\) Put in…