Vectors Question 208
Question: The value of $ \hat{i},\times ,(\hat{i}\times ,\vec{a}),+\hat{j},\times ,(\hat{j}+\vec{a}),+\hat{k}+(,\hat{k}\times \hat{a}) $ is
Options:
A) $ \vec{a} $
B) $ \vec{a},\times ,\hat{k} $
C) $ -2\vec{a} $
D) $ -,\vec{a} $
Correct Answer: C [c] Suppose $ \vec{a},=a_1,\hat{i}+,a_2\hat{j}+,a_3\hat{k} $
Now, $ (\hat{i}\times ,\vec{a}),=a_2,\hat{k},-a_3\hat{j} $
Now, $ \hat{i}\times ,(\hat{i}\times ,\vec{a}),=-a_2,\hat{j}-a_2\hat{k} $
Similarly, $ \hat{j}\times ,(\hat{j}\times ,\vec{a})=-a_1i6-a_3\hat{k}, $
and $ \hat{k},\times ,(\hat{k}\times ,\vec{a}),=-a_1,\hat{i}-a_2\hat{j} $ $ \ Therefore $ $ \hat{i},\times ,(\hat{i}\times \vec{a}),+,\hat{j}\times ,(\hat{j}\times ,\vec{a}),+\vec{k},\times ,(\hat{k}\times ,\vec{a})=-2\vec{a}. $
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Solution:
BETA
