If \( a\) and \( b\) are vectors in space, given by \( a = i - 2 j 5 \) and \( b = 2 i + j + 3 k 14 \) then the value of \((2 a + b)[( a × b)× ( a - 2 b)]\) is

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Question 12

Mathematics Scalar and Vector Products Hard

If \(\vec a\) and \(\vec b\) are vectors in space, given by \(\vec a = \frac {\hat i - 2\hat j}{\sqrt 5}\) and \(\vec b = \frac {2\hat i + \hat j + 3\hat k}{\sqrt {14}}\) then the value of \(\left(2\vec a + \vec b\right)\left[\left(\vec a \times \vec b\right)\times \left(\vec a - 2\vec b\right)\right]\) is

(A) 3

(B) 4

(C) 5

(D) 6

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Correct Solution: Option C

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