ExamBro
ExamBro
TS EAMCET · Maths · Three Dimensional Geometry

The point of intersection of the line joining the points \(\bar{i}+2 \bar{j}+\bar{k}, 2 \bar{i}-\bar{j}-\bar{k}\) and the plane passing through the points \(\bar{i}, 2 \bar{j}, 3 \bar{k}\) is

  1. A \(\bar{i}+2 \bar{j}+3 \bar{k}\)
  2. B \(\frac{1}{7}(3 \bar{i}-\bar{j}+\bar{k})\)
  3. C \(\bar{i}-3 \bar{j}-2 \bar{k}\)
  4. D \(\frac{1}{7}(15 \bar{i}-10 \bar{j}-9 \bar{k})\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{7}(15 \bar{i}-10 \bar{j}-9 \bar{k})\)

Step-by-step Solution

Detailed explanation

Line: \( \bar{r} = (\bar{i}+2 \bar{j}+\bar{k}) + t((2 \bar{i}-\bar{j}-\bar{k}) - (\bar{i}+2 \bar{j}+\bar{k})) \) \( \bar{r} = (1+t)\bar{i} + (2-3t)\bar{j} + (1-2t)\bar{k} \) Plane normal vector:…