Question:
Evaluate \((\vec j-2\vec i)\cdot(\vec k+3\vec i-\vec j)\).
Evaluate \((\vec j-2\vec i)\cdot(\vec k+3\vec i-\vec j)\).
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Arrange vectors as triples \((x,y,z)\) and multiply component-wise.
Updated On: Oct 17, 2025
- \(0\)
- \(-6\)
- \(-7\)
- \(8\)
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The Correct Option is C
Solution and Explanation
Idea. Convert to components and use \( \vec i\cdot\vec i=\vec j\cdot\vec j=\vec k\cdot\vec k=1\) and cross terms \(0\).
\((-2,1,0)\cdot(3,-1,1)=(-2)\cdot3+1\cdot(-1)+0\cdot1=-6-1+0=-7.\)
\((-2,1,0)\cdot(3,-1,1)=(-2)\cdot3+1\cdot(-1)+0\cdot1=-6-1+0=-7.\)
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