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…
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 $\mathrm{A}, \mathrm{B}, \mathrm{C}$
are collinear points
form an isosceles triangle which is not equilateral
form an equilateral triangle
form a scalene triangle
Solution
$\overrightarrow{A B}=\hat{i}+5 \hat{j}-4 \hat{k}, \overrightarrow{B C}=-5 \hat{i}-4 \hat{j}-\hat{k}$
$\overrightarrow{A C}=-4 \hat{i}+\hat{j}-5 \hat{k} \quad \therefore|\overrightarrow{A B}|=|\overrightarrow{B C}|=|\overrightarrow{A C}|=\sqrt{42}$
$\therefore A, B, C$ form an equilateral triangle.