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If the points a(cosalpha+hatisingamma),b...

If the points `a(cosalpha+hatisingamma),b(cosbeta+hatisinbeta) and c(cosgamma+hati sin gamma)` are collinear, then the value of `|z|` is _____ where `z=bc sin(beta-gamma)+ca sin(gamma-alpha)+ab sin(alpha+beta)+3hati`

Text Solution

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The correct Answer is:
3
`|(acosbeta,asinalpha,1),(bcosbeta,bsinbeta,1),(c cosgammac sin gamma,10)|=0`
`impliesbcsin(gamma-beta)+a sin(alpha-gamma)+absin(beta-alpha)=0`
`implies|z|=3`.
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