Consider a vector space with the basis vectors e = +k, = +k and e3 =...

 

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Consider a vector space with the basis vectors e = +k, = +k and e3 = 1 - (not orthonormal) a) Derive the components of vectors a = 2 - 4 + 5k and b = i + 2 - 3k in the new basis (e) by using the reciprocal basis b) Construct matrix G whose elements are defined by the scalar products of the basis vectors, i.e., Gij = j. c) By making use of the results in the previous two parts, calculate the inner product of a i,j=1 and b, i.e., (ab) = {j= a; Gijb;, where a; and b; are the components in the basis d) Calculate the scalar product of a and b using the original Cartesian representation and compare the result with that in part c) Consider a vector space with the basis vectors e = +k, = +k and e3 = 1 - (not orthonormal) a) Derive the components of vectors a = 2 - 4 + 5k and b = i + 2 - 3k in the new basis (e) by using the reciprocal basis b) Construct matrix G whose elements are defined by the scalar products of the basis vectors, i.e., Gij = j. c) By making use of the results in the previous two parts, calculate the inner product of a i,j=1 and b, i.e., (ab) = {j= a; Gijb;, where a; and b; are the components in the basis d) Calculate the scalar product of a and b using the original Cartesian representation and compare the result with that in part c)

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A To derive the components of vectors vec a 2hat i 4hat j 5hat k and vec b hat i 2hat j 3hat k withi... View the full answer