Kinematics Question 289
Question: Three vectors $ \overrightarrow{a},\overrightarrow{b} $ and $ \overrightarrow{c} $ satisfy the relation $ \overrightarrow{a}.\overrightarrow{b}=0 $ and $ \overrightarrow{a}.\overrightarrow{c}=0. $ The vector $ \overrightarrow{a} $ it’s parallel to [AIIMS 1996]
Options:
A) $ \sqrt{29} $ unit
B) $ \sqrt{31} $ unit
C) $ \sqrt{37} $ unit
D) $ \sqrt{41} $ unit
Correct Answer: A $ \vec{v}=\vec{\omega }\times \vec{r} $ $ = \begin{vmatrix} {\hat{i}} & {\hat{j}} & {\hat{k}} \\ 1 & -2 & 2 \\ 0 & 4 & -3 \\ \end{vmatrix} |=\hat{i}(6-8)-\hat{j}(-3)+4\hat{k} $ $ -2\vec{i}+3\vec{j}+4\vec{k} $ $ |\vec{v}|\ =\ \sqrt{{{(-2)}^{2}}+{{(3)}^{2}}+4^{2}} $ $ =\sqrt{29}\ unit $
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