Mathematics | VITEEE 2016 | Discussion Page

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

$3\hat{i}+3\hat{j}$

$3\hat{i}+\hat{j}$

$-\hat{i}+\hat{j}$

$3\hat{i}-3\hat{j}$

Option D

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 = $3\hat{i}-3\hat{j}$

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