ExamBro
ExamBro
TS EAMCET · Maths · Vector Algebra

Let \(\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}\) be two non collinear vectors, \(\mathbf{O P}=x_1 \mathbf{a}+y_1 \mathbf{b}, \mathbf{O Q}=x_2 \mathbf{a}+y_2 \mathbf{b}\) and \(\mathbf{A}^{\prime} \mathbf{O}=\mathbf{O A}, \mathbf{B}^{\prime} \mathbf{O}=\mathbf{O B}\). If \(x_1=\frac{-3}{4}, x_2=\frac{1}{3}\), \(y_1=\frac{7}{4}, y_2=\frac{5}{3}\), then

  1. A \(P\) lies inside the \(\triangle A^{\prime} O B\) and \(Q\) lies outside the \(\triangle A O B\)
  2. B \(P\) lies outside the \(\triangle A O B^{\prime}\) and \(Q\) lies on the \(\triangle A^{\prime} O B^{\prime}\)
  3. C \(P\) lies inside the \(\triangle A O B\) and \(Q\) lies outside the \(\triangle A O B^{\prime}\)
  4. D \(P\) lies on the \(\triangle A^{\prime} O B\) and \(Q\) lies outside the \(\triangle A O B\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(P\) lies inside the \(\triangle A^{\prime} O B\) and \(Q\) lies outside the \(\triangle A O B\)

Step-by-step Solution

Detailed explanation

We have,…