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Vector Analysis Raisinghania Pdf 164l

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is this solution correct i have doubt regarding what should we assume the es i.e. e1,e2 etc. to be. can we say that e_i, i belongs to 1,n or shall we approach via a lengthier method by assuming e_is as basis vectors which are linearly independent. e,g, e1=(1,0,0,0,. ), e2=(0,1,0,0,0,.).. and so on and then getting the following equations on using the linear combination equation with constants c_is: 84d34552a1