Kinematics Question 297
Question: If $ \vec{A} $ and $ \vec{B} $ are perpendicular vectors and vector $ \vec{A}=5\hat{i}+7\hat{j}-3\hat{k} $ and $ \vec{B}=2\hat{i}+2\hat{j}-a\hat{k}. $ The value of a is [EAMCET 1991]
Options:
A) 0
B) $ A^{2}-B^{2} $
C) $ \overrightarrow{B}\times \overrightarrow{A} $
D) $ 2(\overrightarrow{B}\times \overrightarrow{A}) $
Correct Answer: D $ (\vec{A}+\vec{B})\times (\vec{A}-\vec{B}) $ $ =\vec{A}\times \vec{A}-\vec{A}\times \vec{B}+\vec{B}\times \vec{A}-\vec{B}\times \vec{B} $ $ =0-\vec{A}\times \vec{B}+\vec{B}\times \vec{A}-0 $ $ =\vec{B}\times \vec{A}+\vec{B}\times \vec{A}=2(\vec{B}\times \vec{A}) $
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