If the position vector of a particle is r=(3i+4j) meter and its angular velocity is w=(j+2k) rad/sec then its linear velocity (in m/s).
Correct answer: A. (8i-6j+3k)
- A. (8i-6j+3k)
- B. (3i-6j+8k)
- C. (3i-6j+6k)
- D. (6i-8j+3k)
Explanation
To find the linear velocity, you need to take the cross product of the position vector (3i+4j) and the angular velocity (j+2k). This will result in the correct linear velocity. The other options are incorrect because they either misinterpret the relationship between the position vector and the angular velocity or do not consider the correct components in the calculation.
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About Vector Product
The vector product, or cross product, gives a vector perpendicular to two multiplying vectors, with magnitude AB sin θ and direction set by the right-hand rule. It covers properties such as anti-commutation, area from cross products, torque and angular momentum. Unlike the dot product, its result is a vector.
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