E$($X$)/($M$)$E$($M$2)/($P$)($C$)/($B$)()/()($T$)/(212)()/(2024)$

For a system of particles, prove the angular momentum theorem in relative form $-$

$\backslash$sum vec$($M$)\_($A$)=($d$($vec$($H$)\_($rel$))\_($A$))/($dt$)+$mvec$(\backslash$rho $)\_(($G$)/($A$))\backslash$times vec$($a$)\_($A$).$ When is $($d$($vec$($H$)\_($rel$))\_($A$))/($dt$)=\backslash$sum vec$($M$)\_($A$)?$

Here G denotes the center of mass of the system and other notations are used in their common

senses$.$