If the angular momentum of a planet is given by .`vec(L) = 5t^(2)hat(i) - 6that(j) + 3hat(k)`. What is the torque experienced by the planet? Will the torque be in the same direction as that of the angular momentum?

Explanation

The torque experienced by the planet
`vec (tau) = (dvec(L))/(dt) " " [ d/(dt ) (t^(n)) = n^(n-1)] `
`= d/(dt) (5t^(2)hat(i) - 6hat(tj) +3hat(k))`
` = 5 . d/(dt) (t^(2)) hat(i) - 6 d/(dt) (t) hat(j) + 3 d/(dt) (hat(k)) = 10 hat(i) - 6hat(j) + 0 `
`vec(tau) = 10 t hat(i) - 6hat(j)`