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If a⃗=1√103...

Question

If $\to a = \frac{1}{\sqrt{10}} (3^i +^k)$ and $\to b = \frac{1}{7} (2^i + 3^j - 6^k)$ , then the value of $(2 \to a - \to b) \cdot [(\to a \times \to b) \times (\to a + 2 \to b)]$ is?

A

5

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B

0

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C

- 5

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D

- 3

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Solution

The correct option is D $- 5$
$(2 \to a - \to b) \cdot [(\to a \times \to b) \times (\to a + 2 \to b)] \begin{matrix} = (2 \to a - \to b) . {(\to a \times \to b) \times \to a + 2 (\to a \times \to b) \times \to b} = (2 \to a - \to b) . {(\to a . \to a) . \to b - (\to a . \to b) \to a + 2 (\to a . \to b) \to b - 2 (\to b . \to b) . \to a} = (2 \to a - \to b) . (\to b - 2 \to a) = - 4 \to a . \to a - \to b . \to b = - 5 \end{matrix}$

So the value is $- 5$

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