A) \[\sqrt{3}\]
B) \[1\]
C) \[3\]
D) None of the above
Correct Answer: A
Solution :
Given, \[|\vec{u}|=|\vec{v}|=|\vec{w}|=1\] and \[\vec{u}.\vec{v}=\vec{v}.\vec{w}=\vec{w}.\vec{u}=\vec{0}\] (\[\because \] \[\vec{u},\vec{v},\vec{w}\] are mutually perpendicular vector) Now, \[|\vec{u}+\vec{v}+\vec{w}{{|}^{2}}=|\vec{u}{{|}^{2}}+|\vec{v}{{|}^{2}}+|\vec{w}{{|}^{2}}\] \[+2(\vec{u}.\vec{v}+\vec{v}.\vec{w}+\vec{w}.\vec{u})\] \[\Rightarrow \] \[|\vec{u}+\vec{v}+\vec{w}{{|}^{2}}=1+1+1+0=3\] \[\Rightarrow \] \[|\vec{u}+\vec{v}+\vec{w}|=\sqrt{3}\]
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