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
- A \(\mathrm{ABC}\) is a right angled triangle
- B \(\mathrm{ABC}\) is an isosceles triangle
- C \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are collinear points
- D \(\mathrm{ABC}\) is a scalene triangle
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}…
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