A room has dimensions `3m xx 4m xx 5m`. A fly starting at one corner ends up at the diametrocally opposite corner .
(a). What is the magnetic of its displacement ?
(b) Could the length of its path be less than this distance ?
(c) Choosing a situtable cooridinate system find the position vector .
(d) If the fly does not fly but walks , what is the lenght of the shortest path it can take ?

Answer

(a)` sqrt(50)~= 7m`, (b) Never (c) `r= 3hati + 4hatj+5hatk`, (d) `3 + sqrt(41) = 9.4m`]

Explanation

(a) Magnitude of its displacement = diagonal of cuboid.
`" "=sqrt(l^(2) + b^(2)+ h^(2))m`
`" "=sqrt(3^(2) + 4^(2)+ 5^(2))m`
`" "=sqrt(50)m ~= 7m`
(b) Never, because diagonal is shortest distance between corner ends.
(c) Taking initial point as origin position vectors of fly is
`3hati+ 4hatj + 5 hatk`

(d) Lenght of shortest path `= 3m+ sqrt(5^(2) + 4^(2))m`
` " "=3m+ sqrt(41)m`
` " "=3m+ 9.1m`
` " " =9.4`