AP EAMCET · Maths · Vector Algebra
Points \(P\) and \(Q\) are given by \(\overline{O P}=\bar{i}-\bar{j}-\bar{k}\) and \(\overline{O Q}=-\bar{i}+\bar{j}+\bar{k}\). A line along the vector \(\bar{a}=\bar{i}+\bar{j}\) passes through the point \(P\) and another line along the vector \(\bar{b}=\bar{j}-\bar{k}\) passes through the point \(Q\). If a line along the vector \(\bar{c}=\bar{i}-\bar{j}+\bar{k}\) intersects both the lines along the vectors \(\bar{a}\) and \(\bar{b}\) at \(L\) and \(M\) respectively, then \(\overline{P M}=\)
- A \(\bar{i}-\bar{j}+2 \bar{k}\)
- B \(4 \bar{i}+4 \bar{j}\)
- C \(-2 \bar{i}+10 \bar{j}-6 \bar{k}\)
- D \(3 \bar{i}-2 \bar{j}+\bar{k}\)
Answer & Solution
Correct Answer
(C) \(-2 \bar{i}+10 \bar{j}-6 \bar{k}\)
Step-by-step Solution
Detailed explanation
\( \overline{OL} = \overline{OP} + \lambda \bar{a} = (\bar{i}-\bar{j}-\bar{k}) + \lambda (\bar{i}+\bar{j}) \) \( \overline{OM} = \overline{OQ} + \mu \bar{b} = (-\bar{i}+\bar{j}+\bar{k}) + \mu (\bar{j}-\bar{k}) \) \( \overline{OM} - \overline{OL} = k \bar{c} \)…
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