AP EAMCET · Maths · Vector Algebra
Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is
- A \(\frac{19}{5}\)
- B \(\frac{\sqrt{389}}{5}\)
- C \(\frac{\sqrt{341}}{5}\)
- D \(\frac{21}{5}\)
Answer & Solution
Correct Answer
(A) \(\frac{19}{5}\)
Step-by-step Solution
Detailed explanation
Position vector of \(\mathrm{L}\) is \(\frac{2}{5}(-3 \hat{i}-3 \hat{j}+4 \hat{k})\) Position vector of \(\mathrm{M}\) is \(=\frac{3}{5}(4 \hat{i}-4 \hat{j}+3 \hat{k})\) Since \(\overrightarrow{\mathrm{LP}} \|\) and \(\overrightarrow{\mathrm{OB}}\) and…
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