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AP EAMCET · Maths · Vector Algebra

If \(2 \hat{i}+\hat{j}-\hat{k}, \hat{i}-3 \hat{j}+5 \hat{k}\) and \(-3 \hat{i}+4 \hat{j}+4 \hat{k}\) are the position vectors of three points A, B and C respectively, then

  1. A \(\mathrm{ABC}\) is a right angled triangle
  2. B \(\mathrm{ABC}\) is an isosceles triangle
  3. C \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are collinear points
  4. D \(\mathrm{ABC}\) is a scalene triangle
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Answer & Solution

Correct Answer

(D) \(\mathrm{ABC}\) is a scalene triangle

Step-by-step Solution

Detailed explanation

\begin{aligned} \text { (d) } \overrightarrow{O A}=2 \hat{i}+\hat{j}-\hat{k}, \overrightarrow{O B}=\hat{i}-3 \hat{j}+5 \hat{k}, O C=-3 \hat{i}+4 \hat{j}+4 \hat{k} \\ \overrightarrow{A B}=\overrightarrow{O B}-\overrightarrow{O A}=-\hat{i}+4 \hat{j}+6 \hat{k}…