AP EAMCET · Maths · Three Dimensional Geometry
If \(P\) divides the line segment joining the points \(A\) and \(B\) in the ratio \(2: 1\) and the position vectors of \(A\) and \(B\) are \(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}\) and \(-3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}\) respectively, then the position vector of \(p\) is
- A \(\frac{5 \hat{i}-8 \hat{j}}{3}\)
- B \(\frac{-5 \hat{i}+8 \hat{j}}{3}\)
- C \(\frac{5 \hat{i}+8 \hat{j}}{3}\)
- D \(\frac{-5 \hat{i}-8 \hat{j}}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{-5 \hat{i}+8 \hat{j}}{3}\)
Step-by-step Solution
Detailed explanation
It is given that the position vectors of points \(A\) and \(B\) are \(\mathbf{O A}=\hat{\dot{\mathbf{i}}}-2 \hat{\mathbf{j}}\) and \(\mathbf{O B}=-3 \hat{\dot{\mathbf{i}}}+5 \hat{\mathrm{j}}\). So, position vector of point \(P\). Which divides the line segment joining \(A\) and…
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