MCQ
A body is rotating with angular velocity $\omega=(3\hat{\text{i}}-4\hat{\text{j}}-\hat{\text{k}})$ The linear velocity of a point having position vector $\text{r}=(5\hat{\text{i}}-6\hat{\text{j}}+6\hat{\text{k}})$ is:
  • A
    $6\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$
  • B
    $-18\hat{\text{i}}-23\hat{\text{j}}+2\hat{\text{k}}$
  • $-30\hat{\text{i}}-23\hat{\text{j}}+2\hat{\text{k}}$
  • D
    $6\hat{\text{i}}-2\hat{\text{j}}+8\hat{\text{k}}$

Answer

Correct option: C.
$-30\hat{\text{i}}-23\hat{\text{j}}+2\hat{\text{k}}$
$\text{As, v}=\omega\times\text{r}=\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}}\\3&-4&-1\\5&-6&6\end{vmatrix}$
$=\hat{\text{i}}(-24-6)+\hat{\text{j}}(-5-18)+\hat{\text{k}}(-18+20)$
$=-30\hat{\text{i}}-23\hat{\text{j}}+2\hat{\text{k}}$

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