A rectangular plate in the x-y plane is shown in the figure. A force `bar(F) = 2hat(i) - 3 hat(j)` N is applied at point B. Find the torque of `bar(F)` about
(a) the origin O
(b) the point C
(c) X-axis, Y-axis and Z-axis.

Explanation

(a) Torque of `vec(F)` about O : `vec(r) = Ovec(B)=hat(i) + 2hat(j)`
`tau_(0) = vec(r) xx vec(F) = (hat(i) + 2 hat(j)) xx (2 hat(i) - 3 hat(j)) =-7 hat(k) N-m`
(b) `tau_(C) = bar(CB) xx vec(F) = 2 hat(j) xx (2 hat(i) - 3 hat(j)) =- 4 hat(k) N-m`
(c) `tau_(XX.) = vec(tau)_(0).hat(i) = (-7 hat(k)). hat(i) = 0`
`tau_(YY) = vec(tau)_(0). hat(j) = (-7hat(k)).hat(j) = 0`
`tau_(ZZ) = vec(tau)_(0).hat(k) = (-7 hat(k)).hat(k) =- 7 N-m`