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Point A has position vector $\hat i + \hat j - \hat k$ and point B has $2\hat i - \hat j + \hat k$ , Forces $\hat i + \hat j + \hat k$ And $-\hat i - \hat j - \hat k$ are acting on A and B , Then magnitude of moment will be
Option: 1
$\sqrt {11}$

Option: 2
$\sqrt {12}$

Option: 3
$\sqrt {13}$

Option: 4
$\sqrt {14}$

Answers (1)

best_answer

As we have learned

Applications of Vectors -

$\vec{M}=\left ( \vec{r}_{1}-\vec{r}_{2} \right )\times \vec{F}$

- wherein

$\vec{r}_{1}$ and $\vec{r}_{2}$ are position vector's of the point of the application of the forces $\vec{F}$ and $-\vec{F}$ .

$|\vec M| = |(\vec r_1-\vec r_2)\times \vec F|$

$\vec r_1-\vec r_2= \hat i - 2\hat j$

$(\vec r_1-\vec r_2)\times \vec F= (\hat i-2\hat j ) \times (\hat i + \hat j+ \hat k)$

$=\begin{vmatrix} \hat i & \hat j & \hat k \\ 1 & -2 & 0\\ 1&1 &1 \end{vmatrix} = -2 \hat i -\hat j +3 \hat k$

$|(\vec r_1-\vec r_2)\times \vec F|=\sqrt{4+1+9}= \sqrt{14}$

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SANGALDEEP SINGH

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