Discussion Forum

 The moment about the point  $\hat{i}+2\hat{j}+3\hat{k}$ of a force represented by  $\hat{i}+\hat{j}+\hat{k}$ acting through the point  $2i+3j+k$  is 

Answer:

Explanation:

 Here,   $r= (2\hat{i}+3\hat{j}+\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})$

 $\Rightarrow$    $ r=\hat{ i}+\hat{j}-2\hat{k}$   and

$ F=\hat{ i}+\hat{j}+\hat{k}$

 Then, the required moment is given by

 $ r\times F$ = $(\hat{i}+\hat{j}-2\hat{k} ) $ $ \times$

$( \hat{i}+\hat{j}+\hat{k})$

 $\begin{bmatrix}\hat{i} & \hat{j}&\hat{k} \\1 & 1 &-2\\1&1&1 \end{bmatrix}=3\hat{i}-3\hat{j}$

$\therefore$ moment about given point = $3\hat{i}-3\hat{j}$