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Question: What is the value of linear velocity, if \(\overrightarrow{\omega} = 3\widehat{i} - 4\widehat{j} + \...

What is the value of linear velocity, if ω→=3i^−4j^+k^\overrightarrow{\omega} = 3\widehat{i} - 4\widehat{j} + \widehat{k} and r→=5i^−6j^+6k^\overrightarrow{r} = 5\widehat{i} - 6\widehat{j} + 6\widehat{k}

A

6i^−2j^+3k^6\widehat{i} - 2\widehat{j} + 3\widehat{k}

B

6i^−2j^+8k^6\widehat{i} - 2\widehat{j} + 8\widehat{k}

C

4i^−13j^+6k^4\widehat{i} - 13\widehat{j} + 6\widehat{k}

D

−18i^−13j^+2k^- 18\widehat{i} - 13\widehat{j} + 2\widehat{k}

Answer

−18i^−13j^+2k^- 18\widehat{i} - 13\widehat{j} + 2\widehat{k}

Explanation

Solution

v→=ω→×r→=∣i^j^k^3−415−66∣=−18i^−13j^+2k^\overrightarrow{v} = \overrightarrow{\omega} \times \overrightarrow{r} = \left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 3 & - 4 & 1 \\ 5 & - 6 & 6 \end{matrix} \right| = - 18\widehat{i} - 13\widehat{j} + 2\widehat{k}