MHT CET · Maths · Three Dimensional Geometry
The position vector of a point that divides the line segment joining \(\mathrm{P} \equiv(1,2,-1)\) and \(\mathrm{Q} \equiv(-1,1,1)\) externally in the ratio \(1: 2\), is
- A \(3 \hat{i}-3 \hat{k}\)
- B \(3 \hat{i}+3 \hat{j}-3 \hat{k}\)
- C \(-3 \hat{i}+3 \hat{k}\)
- D \(3 \hat{i}+\hat{j}+3 \hat{k}\)
Answer & Solution
Correct Answer
(B) \(3 \hat{i}+3 \hat{j}-3 \hat{k}\)
Step-by-step Solution
Detailed explanation
Using section formula for external division
\(\left(\frac{1 \times(-1)-2 \times 1}{1-2}, \frac{1 \times 1-2 \times 2}{1-2}, \frac{1 \times 1-2 \times(-1)}{1-2}\right)\) \(\equiv(3,3,-3)\)
\(\equiv 3 \hat{i}+3 \hat{j}-3 \hat{k}\)
\(\left(\frac{1 \times(-1)-2 \times 1}{1-2}, \frac{1 \times 1-2 \times 2}{1-2}, \frac{1 \times 1-2 \times(-1)}{1-2}\right)\) \(\equiv(3,3,-3)\)
\(\equiv 3 \hat{i}+3 \hat{j}-3 \hat{k}\)
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