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
- A \(35\)
- B \(30\)
- C \(25\)
- D \(4\)
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…
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