A) Right angled triangle
B) Isosceles triangle
C) Equilateral triangle
D) Collinear
Correct Answer: C
Solution :
Here,\[\overrightarrow{OA}=2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\] \[\overrightarrow{OB}=3\mathbf{i}+4\mathbf{j}+2\mathbf{k}\] \[\overrightarrow{OC}=4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] So, \[\overrightarrow{AB}=\mathbf{i}+\mathbf{j}-2\mathbf{k},\] \[\overrightarrow{BC}=\mathbf{i}-2\mathbf{j}+\mathbf{k}\], \[\overrightarrow{CA}=2\mathbf{i}-\mathbf{j}-\mathbf{k}\] Clearly \[|AB|\,=\,|BC|\,=\,|CA|\,=\sqrt{6}\] So these points are vertices of an equilateral triangle.You need to login to perform this action.
You will be redirected in
3 sec