1.

`lambda` के किस मान के लिए सदिश `lambdahai+(1+lambda)hatj+(1+2lambda)hatk` और `(1-lambda)hati+lambdahatj+2hatk` परस्पर लम्ब हैA. `-(1//3)`B. `1//3`C. `2//3`D. 1

Answer» Correct Answer - A
माना `a=lambdai+(1+lambda)hatj+(1+2lambda)hatk`
तथा `b=(1-lambda)hati+._(1)lambdahatj+2hatk`
अब, a तथा b के परस्पर लम्ब होने के लिए, `a.b=|a||b|cos""(pi)/(2)=0`
`Rightarrow [lambdahati+(1+lambda)hatj+(1+2lambda)hatk]`
`[(1-lambda)hati+lambdaj+2hatk]=0`
`Rightarrow lambda(1-lambda)+(1+lambda)lambda+(1+2lambda)2=0`
`Rightarrow lambda-lambda^(2)+lambda+lambda^(2)+2+4lambda=0`
`Rightarrow 2+6lambda=0 Rightarrow 6lambda=0`
`Rightarrow lambda=-(2)/(6)=(1)/(3)`
`therefore lambda=-(1)/(3)`


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