Question: Let 1, 2, 3 be a given positively oriented ON base in space. Define a new basis f1, f2, f3 by e - e2

Let 1, 2, 3 be a given positively oriented ON base in

Let 1, 2, 3 be a given positively oriented ON base in space. Define a new basis f1, f2, f3 by e - e2 + z e3, f2 = ze+ ze2 + z e3 f the conditions f3 = + + 3. Show that f1, f2, f3 is also an ON basis. (This reasoning does not need to be submitted). Further calculate the determinant of the transition matrix T. = det(T) = ( ). Is this base positively or negatively oriented?

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