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AP EAMCET · Maths · Vector Algebra

Let \(\overline{\mathrm{i}}-2 \overline{\mathrm{j}}+\overline{\mathrm{k}}, \overline{\mathrm{i}}+\overline{\mathrm{j}}-2 \overline{\mathrm{k}}, 2 \overline{\mathrm{i}}-\overline{\mathrm{j}}-\overline{\mathrm{k}}\) and \(\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}}\) be the position vectors of four points \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D respectively. If a point P divides AB in the ratio \(2: 1\) internally and a point \(Q\) divides \(C D\) in the ratio \(1: 2\) externally, then the ratio in which the point with position vector \(5 \overline{\mathrm{i}}-6 \overline{\mathrm{j}}-5 \overline{\mathrm{k}}\) divides PQ is

  1. A \(2: 1\)
  2. B \(-2: 1\)
  3. C \(2: 3\)
  4. D \(-2: 3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(-2: 1\)

Step-by-step Solution

Detailed explanation

\( \overline{p} = \frac{1(\overline{i}-2 \overline{j}+\overline{k}) + 2(\overline{i}+\overline{j}-2 \overline{k})}{3} = \overline{i} - \overline{k} \)…