If `m_(1), m_(2), m_(3)` and `m_(4)` are respectively the magnitudes of the vectors
`a_(1)=2hati-hatj+hatk, a_(2)=3hati-4hatj-4hatk, a_(3)=hati+hatj-hatk` and `a_(4)=-hati+3hatj+hatk`, then the correct order of `m_(1),m_(2),m_(3)` and `m_(4)` is

Options

A. `m_(3)ltm_(1)ltm_(4)ltm_(2)`
B. `m_(3)ltm_(1)ltm_(2)ltm_(4)`
C. `m_(3)ltm_(4)ltm_(1)ltm_(2)`
D. `m_(3)ltm_(4)ltm_(2)ltm_(1)`

Answer

A

Explanation

Given, `m_(1)=|a_(1)|=sqrt(2^(2)+(-1)^(2)+(1)^(2))=sqrt(6)`
`m_(2)=|a_(2)|=sqrt(3^(2)+(-4)^(2)+(-4)^(2))=sqrt(41)`
`m_(3)=|a_(3)|=sqrt(1^(2)+1^(2)+(-1)^(2))=sqrt(3)`
and `m_(4)=|a_(4)|=sqrt((-1)^(2)+(3)^(2)+(1)^(2))=sqrt(11)`
`therefore m_(3)ltm_(1)ltm_(4)ltm_(2)`