TS EAMCET · Maths · Three Dimensional Geometry
\(P\) and \(Q\) are the points of trisection of the line segment \(A B\). If \(2 \hat{i}-5 \hat{j}+3 \hat{k}\) and \(4 \hat{i}+\hat{j}-6 \hat{k}\) are the position vectors of \(A\) and \(B\) respectively, then the position vector of the point which divides \(P Q\) in the ratio \(2: 3\) is
- A \(\frac{1}{15}(44 \hat{i}-33 \hat{j}-18 \hat{k})\)
- B \(\frac{1}{5}(36 \hat{i}-26 \hat{j}-18 \hat{k})\)
- C \(\frac{1}{5}(3 \hat{i}+7 \hat{j}-9 \hat{k})\)
- D \(\frac{1}{15}(-3 \hat{i}-7 \hat{j}+9 \hat{k})\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{15}(44 \hat{i}-33 \hat{j}-18 \hat{k})\)
Step-by-step Solution
Detailed explanation
\(P Q\) trisect \(A B\); and \(R\) divides \(P Q\) in the ratio \(2: 3\). Let's assume \(A B\) line segment of length 3 units. \(P R\) and \(R Q \equiv \frac{2}{5}\) and \(\frac{3}{5} \Rightarrow A R=1+\frac{2}{5}, R B=1+\frac{3}{5}\)…
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