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Let \(\vec{a}=\hat{i}+\hat{j}+2\hat{k}\) and \(\vec{b}=-\hat{i}+2\hat{j}+3\hat{k}\). Then the vector product \((\vec{a}+…

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Let \(\vec{a}=\hat{i}+\hat{j}+2\hat{k}\) and \(\vec{b}=-\hat{i}+2\hat{j}+3\hat{k}\). Then the vector product \((\vec{a}+\vec{b})\times ((\vec{a}\times ((\vec{a}-\vec{b})\times \vec{b}))\times \vec{b})\) is equal to:

[JEE Main 2021, 27 Jul (Shift 1)]

a

\(5(34\hat{i}-5\hat{j}+3\hat{k})\)

b

\(5(30\hat{i}-5\hat{j}+7\hat{k})\)

c

\(7(30\hat{i}-5\hat{j}+7\hat{k})\)

d

\(7(34\hat{i}-5\hat{j}+3\hat{k})\)

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