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_(B)|=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)`