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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

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

C

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

D

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

Answer

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

Explanation

Solution

v⃗=ω⃗×r⃗=∣i^J^k^3−415−66∣\vec { v } = \vec { \omega } \times \vec { r } = \left| \begin{array} { r r r } \hat { i } & \hat { J } & \hat { k } \\ 3 & - 4 & 1 \\ 5 & - 6 & 6 \end{array} \right| v→=(−24+6)i−(18−5)J^+(−18+20)k^\overrightarrow{v} = ( - 24 + 6)i - (18 - 5)\widehat{J} + ( - 18 + 20)\widehat{k}

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