The position of a particle moving in space varies with time `t` according as `:-`
`x(t)=3 cosomegat`
`y(t)=3sinomegat`
`z(t)=3t-8`
where `omega` is a constant. Minimum distance of particle from origin is `:-`

Options

A. `1` unit
B. `2` unit
C. `3` unit
D. `4` unit

Answer

C

Explanation

Distance from origin, `r=sqrt(x^(2)+y^(2)+z^(2))`
`=sqrt(9cos^(2)omegat+9sin^(2)omegat+(4t-8)^(2)`
`=sqrt(9+(4t-8)^(2)`
For minimum `t,4t-8=0rArr1=2` unit
`rArrr_(min)=3units`