Kinematics Question 761
Question: What is the value of linear velocity, if $ \vec{\omega }=3\hat{i}-4\hat{j}+\hat{k} $ and $ \vec{r}=5\hat{i}-6\hat{j}+6\hat{k} $ [Pb. PMT 2000]
Options:
A)$ 6\hat{i}+2\hat{j}-3\hat{k} $
B)$ -18\hat{i}-13\hat{j}+2\hat{k} $
C) $ 4\hat{i}-13\hat{j}+6\hat{k} $
D)$ 6\hat{i}-2\hat{j}+8\hat{k} $
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Answer:
Correct Answer: B
Solution:
$ \overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$
= $\begin{vmatrix}\hat{i} & \hat{j} & \hat{k}\\3 & -4 & 1\\5 & -6 & 6\\ \end{vmatrix} $
=$-18\hat{i}-13\hat{j}+2\hat{k} $
