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NDA 2021 Maths · Mathematics · Vector Algebra · medium

The moment about the origin of the force hat i+2hat j+3hat k acting at the point with position vector hat i+hat j is

Single correct option

The moment about the origin of the force i^+2j^+3k^\hat i+2\hat j+3\hat k acting at the point with position vector i^+j^\hat i+\hat j is
  1. A. −3i^+3j^−k^-3\hat i+3\hat j-\hat k
  2. B. 3i^−3j^+k^3\hat i-3\hat j+\hat k
  3. C. 3i^+3j^+k^3\hat i+3\hat j+\hat k
  4. D. i^+2j^\hat i+2\hat j
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Answer: (B) 3i^−3j^+k^3\hat i-3\hat j+\hat k

Moment =r⃗×F⃗=∣i^j^k^110123∣=(3−0)i^−(3−0)j^+(2−1)k^=3i^−3j^+k^=\vec r\times\vec F=\begin{vmatrix}\hat i&\hat j&\hat k\\1&1&0\\1&2&3\end{vmatrix}=(3-0)\hat i-(3-0)\hat j+(2-1)\hat k=3\hat i-3\hat j+\hat k. Reversing the order gives the negative.
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