What is the linear velocity if angular velocity vector ω = 3î − 4ĵ + k̂ and position vector r = 5î − 6ĵ + 6k̂

6î + 2ĵ − 3k̂
−18î − 13ĵ + 2k̂
18î + 13ĵ − 2k̂
6î − 2ĵ + 8k̂

Correct answer: 18î + 13ĵ − 2k̂

Solution

The linear velocity is given by the cross product of angular velocity (ω) and position vector (r): v = ω × r. Calculating the cross product, we get v = |î ĵ k̂| |3 -4 1| |5 -6 6| = 18î + 13ĵ − 2k̂.

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