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NIMCET 2008

A rigid body is rotating at the rate of $3$ radians per second about an axis $AB$, where $A(1,-2,1)$ and $B(3,-4,2)$. The velocity of the point $P(5,-1,-1)$ of the body is

Solution

Direction vector of axis $\vec{AB}=(2,-2,1)$ Unit vector along axis $\hat n=\dfrac{(2,-2,1)}{3}$ Angular velocity $\vec\omega=3\hat n=(2,-2,1)$ Position vector of $P$ relative to $A$: $\vec r=(4,1,-2)$ Velocity $\vec v=\vec\omega\times\vec r=3\vec i+8\vec j+10\vec k$
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