Kinematics Question 300
Question: The position vectors of radius are $ 2\hat{i}+\hat{j}+\hat{k} $ and $ 2\hat{i}-3\hat{j}+\hat{k} $ while those of linear momentum are $ 2\hat{i}+3\hat{j}-\hat{k}. $ Then the angular momentuM is [BHU 1997]
Options:
A) 8
B) $ 8\sqrt{3} $
C) $ 3\sqrt{8} $
D) 192
Correct Answer: A Area of parallelogram $ =\overrightarrow{A}\times \overrightarrow{B} $ $ =(\hat{i}+2\hat{j}+3\hat{k})\times (3\hat{i}-2\hat{j}+\hat{k}) $ $ = \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & 2 & 3 \\ 3 & -2 & 1 \\ \end{vmatrix} $ $ =(8)\hat{i}+(8)\hat{j}-(8)\hat{k} $ Magnitude $ =\sqrt{64+64+64} $ = $ 8\sqrt{3} $
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