ExamBro
ExamBro
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

  1. A \(\frac{5 \hat{i}-8 \hat{j}}{3}\)
  2. B \(\frac{-5 \hat{i}+8 \hat{j}}{3}\)
  3. C \(\frac{5 \hat{i}+8 \hat{j}}{3}\)
  4. D \(\frac{-5 \hat{i}-8 \hat{j}}{3}\)
Verified Solution

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…