Why is angular displacement vector quantity only for small values? Why is the direction of angular displacement perpendicular to the plane of rotation of object?

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Q. why infinitesimal angular displacement is a vector rather avg angular displacement or velocity a scalar ?!!!

Displacement does not have direction as it is the shortest distance between initial and starting point; then why is displacement a vector quantity and distance a scalar quantity?

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Q. An object is found to rotate with an angular velocity

ω (t) = 5 t + 3

, where

ω

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