Let vectors a and b in space be defined as a = (i - 2j) / sqrt(5) and b = (2i + j + 3k) / sqrt(14). Find the value of (2a + b). [(a x b) x (a - 2b)].

Correct answer: 5

Solution

Since a and b are unit vectors (|a|=1, |b|=1) and a.b = (1*2 + (-2)*1 + 0*3)/(sqrt(5)*sqrt(14)) = 0/sqrt(70) = 0, they are perpendicular. Using the triple product and orthogonality simplifies the expression to 5.

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