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Find the vector perpendicular to the pln...

Find the vector perpendicular to the plne determined by the points P(1,-2,2), Q(2,0,-1 ) and R(0,2,1)

Text Solution

Verified by Experts

`bar(PQ)=("Position vector of Q")-("Position vector of P")`
`=(2hati-hatk)-(hati-hatj+2hatk)=hati+hatj=3hatk`
`"Similarly", bar(P)R=(hat2j+bark)-(hati-hatj+2hatk)=-hati+3hatj+bar(k)`
`therefore |bar(PQ)xxbar(PR)|=sqrt(8^(2)+4^(2)+4^(2))=4sqrt6`
Required unit vectors
`=pm(1)/(4sqrt6)(8hati+4hatj+4hatk)=pm(1)/(sqrt6)(2hati+hatj+8hatk)`
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