A) 7 units
B) \[\sqrt{38}\] units
C) \[\sqrt{155}\] units
D) None of these
Correct Answer: A
Solution :
The length of a diagonal of the parallelepiped is \[\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\], where \[a={{x}_{2}}-{{x}_{1}},\,b={{y}_{2}}-{{y}_{1}}\], \[c={{z}_{2}}-{{z}_{1}}\]. A parallelepiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. Let a, b, c be the lengths of edges, then \[a=5-2=3,\,b=9-3=6\] and \[c=7-5=2\] So, the length of diagonal of a parallelepiped \[=\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}\] \[=\sqrt{9+36+4}=\sqrt{49}=7\] units
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