Question

Two forces f1 = 2i– 5j-6k and F2 =-i +2j - k are acting on a body at the points (1, 1, 0) and (0, 1, 2)
respectively. Find torque acting on the body about point (-1,0,1).​

Answer 1

Answer:

$\vec{\tau}=-14i+10j-9k$

Explanation:

1) We have, position vectors about point (-1,0,1)

$\vec{r_1}=(1i+1j-0k)-(-1i+0j+1k)=2i+1j-1k\\ \\ \vec{r_2}=(0i+1j+2k)-(-1+0j+1k)=1i+1j+1k$

Also,

Force vectors are represented by :

$F_{1}=2i-5j-6k\\ \\F_2=-i+2j-k$

2) Then,

Net Torque is given by :

$\tau=r_{1}\times F_{1}+r_2\times F_{2}$

First we will calculate first term:

$r_1\times F_1=\begin{vmatrix}{}}i&j&k\\2&1&-1\\2&-5&-6\end{vmatrix}\\ \\ \\ =-11i+10j-112k$

Then, we will calculate second term:

$r_2\times F_2=\begin{vmatrix}{}}i&j&k\\1&1&1\\-1&2&-1\end{vmatrix}\\ \\ \\ =-3i+3k$

Then,we will add both the terms to get the resultant torque in vector form.

That is, Resultant torque is

$\tau=-14i+10j-9k$