The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by [MP PET 1993]

The perimeter of the triangle whose vertices have the position vectors

1.	The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by [MP PET 1993]
A.	\[15+\sqrt{157}\]
B.	\[15-\sqrt{157}\]
C.	\[\sqrt{15}-\sqrt{157}\]
D.	\[\sqrt{15}+\sqrt{157}\]
Answer» B. \[15-\sqrt{157}\]

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The perimeter of the triangle whose vertices have the position vectors \[(\mathbf{i}+\mathbf{j}+\mathbf{k}),\,\,(5\mathbf{i}+3\mathbf{j}-3\mathbf{k})\] and \[(2\mathbf{i}+5\mathbf{j}+9\mathbf{k}),\] is given by [MP PET 1993]

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