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If a point P whose position vector is ve...

If a point P whose position vector is `vec a` lying on the plane ABC where `A(2,3,0), B (3,-2,0), C(2,-1,0)`. Then distance of P from plane ABC is given by-

Text Solution

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`vecn=vec(AB)*vec(AC)`
`=(hati-5hatj)*(0hati-4hatj)`
`=-4hatk`
`vec(AP)*vecn=|vec(AP)||vecn|costheta`
`(vecAvecP*vecn)/|(vecn)|=|vec(AP)|costheta`
`(veca-(2hati+3hatj)*hatk=d`
`vec(AP)=veca-vecb`
`d=|(veca-4hatk)/4|=|vecahatk|`
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