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If veca, vecb and vecc be three non-copl...

If `veca, vecb and vecc` be three non-coplanar vectors and a',b' and c' constitute the reciprocal system of vectors, then prove that
`i. vecr=(vecr.veca')veca+(vecr.vecb')vecb+(vecr.vecc')vecc`
ii. `vecr= (vecr.veca)veca'+(vecr.vecb)vecb' + (vecr.vecc) vecc'`

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To prove the given statements regarding the vectors, we will follow a systematic approach. Let's denote the vectors as follows: - Let \(\vec{a}, \vec{b}, \vec{c}\) be three non-coplanar vectors. - Let \(\vec{a}', \vec{b}', \vec{c}'\) be their respective reciprocal vectors. ### Proof for Part (i): We need to prove that: ...
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