AP EAMCET · Maths · Vector Algebra
If \(\hat{i}-2 \hat{j}+3 \hat{k}, 2 \hat{i}+3 \hat{j}+\hat{k},-3 \hat{i}-\hat{j}-2 \hat{k}\) are the position vectors of three points A, B, C respectively, then \(\mathrm{A}, \mathrm{B}, \mathrm{C}\)
- A are collinear points
- B form an isosceles triangle which is not equilateral
- C form an equilateral triangle
- D form a scalene triangle
Answer & Solution
Correct Answer
(C) form an equilateral triangle
Step-by-step Solution
Detailed explanation
\(\overrightarrow{A B}=\hat{i}+5 \hat{j}-4 \hat{k}, \overrightarrow{B C}=-5 \hat{i}-4 \hat{j}-\hat{k}\) \(\overrightarrow{A C}=-4 \hat{i}+\hat{j}-5 \hat{k} \quad \therefore|\overrightarrow{A B}|=|\overrightarrow{B C}|=|\overrightarrow{A C}|=\sqrt{42}\) \(\therefore A, B, C\)…
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