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NEET · Physics · STD 11 - 6. system of particles and rotational motion

બિંદુ \( ( 2,-2,-2 )\)  ને અનુલક્ષીને બિંદુ \(( 2,0,-3 ) \) પર બળ \(\overrightarrow {\;F} = 4\hat i + 5\hat j - 6\hat k\) ની ચાકમાત્રા આપવામાં આવે છે.

  1. A \( - 8\hat i - 4\hat j - 7\hat k{\rm{\;\;\;}}\;\)
  2. B \( - 4\hat i - \hat j - 8\hat k{\rm{\;\;\;}}\)
  3. C \( - 7\hat i - 4\hat j - 8\hat k\)
  4. D \( - 7\hat i - 8\hat j - 4\hat k\)
Verified Solution

Answer & Solution

Correct Answer

(C) \( - 7\hat i - 4\hat j - 8\hat k\)

Step-by-step Solution

Detailed explanation

Moment of the force is, \(\begin{array}{l}
\overrightarrow \tau   = \left( {\overrightarrow r  - \overrightarrow {{r_0}} } \right) \times \overrightarrow F \\
Here,\,\overrightarrow {{r_0}}  = 2\hat i - 2\hat j - 2\hat k\\
and\,\,\overrightarrow r  = 2\hat i + 0\hat j - 3\hat k\\
\therefore \,\overrightarrow r  - \overrightarrow {{r_0}}  = \left( {2\hat i + 0\hat j - 3\hat k} \right) - \left( {2\hat i - 2\hat j - 2\hat k} \right)\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0\hat i + 2\hat j - \hat k\\
\therefore \,\,\,\overrightarrow \tau  \, = \left| \begin{array}{l}
\hat i\,\,\,\,\,\,\hat j\,\,\,\,\,\,\,\,\hat k\\
0\,\,\,\,\,\,2\,\,\,\,\, - 1\\
4\,\,\,\,\,\,5\,\,\,\, - 6
\end{array} \right| =  - 7\hat i - 4\hat j - 8\hat k
\end{array}\)
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