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A particle has an angular speed of 3 ...

A particle has an angular speed of 3 rad/s and the axis of rotation passes through the points `(1,1,2)a n d(1,2,-2)dot` Find the velocity of the particle at point `P(3,6,4)dot`

Text Solution

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`vec(OA)=hati + hatj + 2hatk`
`vec(OB) = hati + 2hatj - 2hatk `
` vec(AB) = hatj -4hatk Rightarrow |vecAB|= sqrt17`
`vec(AP) = (3 veci + 6vecj + 4hatk) - (hati + hatj + 2hatk)`
` = 2hati + 5 hatj + 2 hatk`
`vecomega= 3/sqrt17 (hatj - 4hatk)2`
`vecv = vecomega xxvecr = 3/sqrt17 (hatj - 4hatk) xx ( 2hati + 5 hatj + 2hatk) `
`= 3/sqrt17 (22 hati - 8hatj - 2hatk)`
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