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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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