ExamBro
ExamBro
AP EAMCET · Maths · Three Dimensional Geometry

The vector equation of a plane passing through the line of intersection of the planes \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}-2 \overline{\mathrm{k}})=3, \overline{\mathrm{r}} \cdot(2 \overline{\mathrm{j}}+\overline{\mathrm{k}})=5\) and the point \(\overline{\mathrm{i}}+2 \overline{\mathrm{j}}+3 \overline{\mathrm{k}}\) is

  1. A \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}+4 \overline{\mathrm{j}})=13\)
  2. B \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}+6 \overline{\mathrm{j}}+\overline{\mathrm{k}})=18\)
  3. C \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}+2 \overline{\mathrm{j}}-\overline{\mathrm{k}})=8\)
  4. D \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}+8 \overline{\mathrm{j}}+2 \overline{\mathrm{k}})=23\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}+8 \overline{\mathrm{j}}+2 \overline{\mathrm{k}})=23\)

Step-by-step Solution

Detailed explanation

\( (\overline{\mathrm{r}} \cdot(\overline{\mathrm{i}}-2 \overline{\mathrm{k}})-3) + \lambda (\overline{\mathrm{r}} \cdot(2 \overline{\mathrm{j}}+\overline{\mathrm{k}})-5) = 0 \)…