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}) $

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Answer:

Correct Answer: D

Solution:

$ (\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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