Kinematics Question 261
Question: If $ \overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C}, $ then which of the following statements it’s wrong
Options:
A) $ \overrightarrow{C}\bot \overrightarrow{A} $
B) $ \overrightarrow{C}\bot \overrightarrow{B} $
C) $ \overrightarrow{C}\bot (\overrightarrow{A}+\overrightarrow{B}) $
D) $ \overrightarrow{C}\bot (\overrightarrow{A}\times \overrightarrow{B}) $
Correct Answer: D From the property of vector product, we notice that $ \overrightarrow{C} $ must be perpendicular to the plane formed by vector $ \overrightarrow{A} $ and $ \overrightarrow{B} $ . Thus $ \overrightarrow{C} $ is perpendicular to both $ \overrightarrow{A} $ and $ \overrightarrow{B} $ and $ (\overrightarrow{A}+\overrightarrow{B}) $ vector also, must lie in the plane formed by vector $ \overrightarrow{A} $ and $ \overrightarrow{B} $ . Thus $ \overrightarrow{C} $ must be perpendicular to $ (\overrightarrow{A}+\overrightarrow{B}) $ also but the cross product $ (\overrightarrow{A}\times \overrightarrow{B}) $ gives a vector $ \overrightarrow{C} $ which can not be perpendicular to it’self. Thus the last statement it’s wrong.Show Answer
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