Question

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

• A. $4i-13j+6k$
• B. $-18i-13j+2k$
• C. $6i+2j-3k$
• D. $6i-2j+8k$

Answer 1

The correct option is B

$-18i-13j+2k$

Step 1: Given data

The radius vector, $r=3i-4j+k$

Angular velocity vector, $\omega =5i-6j+6k$

Step 2: Formula used

The mathematical expression for calculating linear velocity is given as follows:

$v=r\times \omega ...\left(1\right)$

Where, $\omega$ is the angular velocity, $r$ is the radius, and $v$ is the linear velocity.

Step 3: Calculation

Substitute the values in equation (1).

$$\begin{gathered} v=r\times \omega \\ v=\left(3i-4j+k\right)\times \left(5i-6j+6k\right) \end{gathered}$$

$$\begin{gathered} v=\left|\begin{array}{ccc}i& j& k\\ 3& -4& 1\\ 5& -6& 6\end{array}\right| \\ v=(-24+6)i-(18-5)j+(-18+20)k \\ v=-18i-13j+2k \end{gathered}$$

Hence, option B is correct.