`lambda ` का मान ज्ञात कीजिए यदि सदिश `2hati -hatj +hatk ,hati +2hatj -hatk ` तथा ` 3hati +lambdahatj +5hatk ` एक समतलीय है|

Explanation

माना `oversetto A=2hati -hatj +hatk `
` oversetto B =hati +2hatj -hatk `
`oversetto C =3hati +lambda hatj +5hatk `
सदिश `oversetto A,oversetto B,oversetto C` एक समतलीय होंगे यदि `[oversetto Aoversetto B oversetto C ]=0`
अब `[vecA vec B vecC]=|{:(2,-1,1),(1,2,-1),(3,lambda,5):}|=0`
` rArr " " 2(10 +lambda )+ 1(5+3) + 1(lambda -6 )=0 `
` " "20 + 2lambda +8+lambda -6=0`
` " "3lambda +22=0`
` " "lalmbda =-(22)/(3)`