Kinematics Question 442
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}) $ it’s
Options:
A) $ \vec{a} $
B) $ \vec{a}\times \hat{k} $
C) $ -2\vec{a} $
D) $ -\vec{a} $
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Answer:
Correct Answer: C
Solution:
[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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