A physical quantity which has a direction:-

Answer

(i) `36hat(i)-144 t hat(j)` (ii) `(-288 t^(3)+864 t^(2)) hat(k)` (iii) `(36t-36)hat(i)-72 t^(2) hat(j)` (iv) `-72 t^(4)+288 t^(3)hat(k)`

Explanation

`vecv=(dvecr)/(dt)=(6t-6)hati+(-12t^2)hatj m//s`
`a=(dvecr)/(dt)=(6t-24tjatj)m//s^2`
(i)`vecF=mveca=6(6hati-24hatj)=(36hati-144thatj)N`
(ii)`vectau=vecrxxvecF=[(3t^2-6t)hati+(-4t^3)hatj]xx[36hati-144thatj]`
`=[(-144xx3t^2)+(144xx6t^2)+144t^3]hatk`
`=(-288t^3+864t^2)hatk`
(iii)`vecp=mvecv=6[(6t-6)hati+(-12t^2)hatj]`
`[36(t-1)hati-72t^2hatj]`
(iv)`vecL=vecrxxvecp=[(3t^2-6t)hati+(-4t^3)hatj]xx[36(t-1)hati-72t^2hatj]`
`=[-72t^4+288t^3]hatk`