A) Are collinear
B) Form an equilateral triangle
C) Form a scalene triangle
D) Form a right angled triangle
Correct Answer: B
Solution :
Let \[P,\,Q\] and \[R\] be points having position vectors \[\alpha \,\mathbf{i}+\beta \,\mathbf{j}+\gamma \,\mathbf{k},\] \[\beta \,\mathbf{i}+\gamma \,\mathbf{j}+\alpha \,\mathbf{k}\] and \[\gamma \,\mathbf{i}+\alpha j+\beta \mathbf{k}\] respectively. Then,\[|\overrightarrow{PQ}|\,=\,|\overrightarrow{QR}|\,=\,|\overrightarrow{RP}|\,=\sqrt{{{(\alpha -\beta )}^{2}}+{{(\beta -\gamma )}^{2}}+{{(\gamma -\alpha )}^{2}}}\] Hence \[\Delta PQR\] is an equilateral triangle.
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