InterviewSolution
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InterviewSolution
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If ` vec a , vec b , vec c`are three mutually perpendicular unit vectors,then prove that `| vec a+ vec b+ vec c|=sqrt(3)`A. 1B. `sqrt(2)`C. `sqrt(3)`D. 2 |
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Answer» Correct Answer - C Given `a^(2)=b^(2)=c^(2)=1 and vec(a).vec(b)=vec(b).vec(c)=vec(c).vec(a)=0`. `:. |vec(a)+vec(b)+vec(c)|^(2)=(vec(a)+vec(b)+vec(c)).(vec(a)+vec(b)+vec(c))` `=vec(a).vec(a)+vec(b).vec(b)+vec(c).vec(c)+2(vec(a).vec(b)+vec(b).vec(c)+vec(c).vec(a))` `=a^(2)+b^(2)+c^(2)+2xx0=(1+1+1+0)=3`. Hence, `|vec(a)+vec(b)+vec(c)|=sqrt(3)`. |
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