A) Equilateral
B) Isosceles
C) Scalene
D) Right angled and isosceles also
Correct Answer: D
Solution :
Given, position vectors of \[A,B\] and C are \[7\mathbf{j}+10\mathbf{k}\], \[-\mathbf{i}+6\mathbf{j}+6\mathbf{k}\] and \[-4\mathbf{i}+9\mathbf{j}+6\mathbf{k}\]respectively. \ \[|\overrightarrow{AB}|=|-\mathbf{i}-\mathbf{j}-4\mathbf{k}|=\sqrt{18}\] \[|\overrightarrow{BC}|=|-3\mathbf{i}+3\mathbf{j}|=\sqrt{18}\] \[|\overrightarrow{AC}|=|-4\mathbf{i}+2\mathbf{j}-4\mathbf{k}|=\sqrt{36}\] Clearly, \[AB=BC\] and \[{{(AC)}^{2}}={{(AB)}^{2}}+{{(BC)}^{2}}\] Hence, triangle is right angled isosceles.
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