A) Form an isosceles triangle
B) Form a right-angled triangle
C) Are collinear
D) Form a scalene triangle
Correct Answer: C
Solution :
\[\overrightarrow{AB}=(3-2)\mathbf{i}+(-2-1)\mathbf{j}+(1+1)\mathbf{k}=\mathbf{i}-3\mathbf{j}+2\mathbf{k}\] \[\overrightarrow{BC}=(1-3)\mathbf{i}+(4+2)\mathbf{j}+(-3-1)\mathbf{k}=-2\mathbf{i}+6\mathbf{j}-4\mathbf{k}\] \[\overrightarrow{CA}=(2-1)\mathbf{i}+(1-4)\mathbf{j}+(-1+3)\mathbf{k}=\mathbf{i}-3\mathbf{j}-2\mathbf{k}\] \[|\overrightarrow{AB}|\,=\sqrt{1+9+4}=\sqrt{14}\] \[|\overrightarrow{BC}|\,=\sqrt{4+36+16}=\sqrt{56}=2\sqrt{14}\] \[|\overrightarrow{CA}|\,=\sqrt{1+9+4}=\sqrt{14}\] So, \[|\overrightarrow{AB}|+|\overrightarrow{AC}|=\,|\,\overrightarrow{BC}\,|\] and angle between AB and BC is 180°. Points A, B, C cannot form an isosceles triangle. Hence A, B, C are collinear.You need to login to perform this action.
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