The velocitities of three particles A, B and C are `vec(v_(A))=(3hati-5hatj+2hatk)ms^(-1), vec(v_(B))=(hati+2hatj+3hatk)ms^(-1)` and `vec(v_(C))=(5hati+3hatj+4hatk)ms^(-1)`, respectively. Which particle travels at neither greatest nor lowest speed?

Explanation

We know that speed is the magnitude of the velocity vector. Hence,
Speed of A `=|vecV_(A)|= sqrt((3)^2+(-5)^2+(2)^2)`
`= sqrt(9+25+4) = sqrt(38) ms^(-1)`
Speed of B `=|vecV_(B)| = sqrt((1)^2+(2)^2+(3)^2)`
`=sqrt(1+4+9) = sqrt(14) ms^(-1)`
Speed of C `=|vecV_(C )|= sqrt((5)^2+(3)^2+(4)^2)`
`=sqrt(25+9+16) = sqrt(50) ms^(-1)`
The particle C has the greatest speed.
`= sqrt(50) gt sqrt(38) gt sqrt(14)`.