AP EAMCET · Maths · Three Dimensional Geometry
\(\bar{i}-2 \bar{j}\) is a point on the line parallel to the vector \(2 \bar{i}+\bar{k}\). If \(\bar{i}+2 \bar{j}\) is a point on the plane parallel to the vectors \(2 \bar{j}-\bar{k}\) and \(\bar{i}+2 \bar{k}\), then the point of intersection of the line and the plane is
- A \(-\frac{1}{3}(\bar{i}+6 \bar{j}+2 \bar{k})\)
- B \(\frac{1}{3}(\bar{i}+6 \bar{j}+2 \bar{k})\)
- C \(-\frac{1}{3}(\bar{i}-6 \bar{j}+2 \bar{k})\)
- D \(\frac{1}{3}(\bar{i}-6 \bar{j}+2 \bar{k})\)
Answer & Solution
Correct Answer
(A) \(-\frac{1}{3}(\bar{i}+6 \bar{j}+2 \bar{k})\)
Step-by-step Solution
Detailed explanation
Equation of line: \( \mathbf{r} = (\bar{i}-2 \bar{j}) + t (2 \bar{i}+\bar{k}) = (1+2t)\bar{i} - 2\bar{j} + t\bar{k} \) Normal vector to plane:…
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