Find the value of (2a→+2b→)×(2a→−2b→)=

(2a¯+2b¯)×(2a¯−2b¯)=4a¯×a¯−4a¯×b¯+4b¯×a¯−4(b¯×b¯)=−4a¯×b¯−4a¯×b¯=−8a¯×b¯

Find the value of (2a→+2b→)×(2a→−2b→)=

(2a¯+2b¯)×(2a¯−2b¯)=4a¯×a¯−4a¯×b¯+4b¯×a¯−4(b¯×b¯)=−4a¯×b¯−4a¯×b¯=−8a¯×b¯

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Find the value of $(2 \vec{a} + 2 \vec{b}) \times (2 \vec{a} - 2 \vec{b}) =$

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$(\vec{a} \times \vec{b})$

$2 (\vec{a} \times \vec{b})$

$- 8 (\vec{a} \cdot \vec{b})$

$- 8 (\vec{a} \times \vec{b})$

answer is D.

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Detailed Solution

$\begin{matrix} (2 \bar{a} + 2 \bar{b}) \times (2 \bar{a} - 2 \bar{b}) = 4 (\bar{a} \times \bar{a}) - 4 (\bar{a} \times \bar{b}) + 4 (\bar{b} \times \bar{a}) - 4 (\bar{b} \times \bar{b}) \\ = - 4 (\bar{a} \times \bar{b}) - 4 (\bar{a} \times \bar{b}) = - 8 (\bar{a} \times \bar{b}) \end{matrix}$