What is the value of linear velocity if overr | vedclass

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Question

(B) The linear velocity $\overrightarrow{v}$ is given by the cross product of angular velocity $\overrightarrow{\omega}$ and position vector $\overrig

Vedclass · Accepted Answer

$-2\widehat{i} + 45\widehat{j} - 29\widehat{k}$

Vedclass · Answer

(B) The linear velocity $\overrightarrow{v}$ is given by the cross product of angular velocity $\overrightarrow{\omega}$ and position vector $\overrightarrow{r}$:$\overrightarrow{v} = \overrightarrow{\omega} 	imes \overrightarrow{r}$$\overrightarrow{v} = \begin{vmatrix} \widehat{i} & \widehat{j} & \widehat{k} \ -5 & 3 & 5 \ 3 & 4 & 6 \end{vmatrix}$Expanding the determinant:$\overrightarrow{v} = \widehat{i}(3 	imes 6 - 5 	imes 4) - \widehat{j}(-5 	imes 6 - 5 	imes 3) + \widehat{k}(-5 	imes 4 - 3 	imes 3)$$\overrightarrow{v} = \widehat{i}(18 - 20) - \widehat{j}(-30 - 15) + \widehat{k}(-20 - 9)$$\overrightarrow{v} = -2\widehat{i} + 45\widehat{j} - 29\widehat{k}$

What is the value of linear velocity if $\overrightarrow{r} = 3\widehat{i} + 4\widehat{j} + 6\widehat{k}$ and $\overrightarrow{\omega} = -5\widehat{i} + 3\widehat{j} + 5\widehat{k}$?

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