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If 2hati-3hatj+4hatk and 3hati+lambdahat...

If `2hati-3hatj+4hatk` and `3hati+lambdahatj+muhatk` be collinear vectors, them find the values of `lambda` and `mu`.

Text Solution

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Let `hatalpha=2hati-3hatj+4hatk` and `hatb=3hati+lambdahatj+muhatk`
Given `hata & hatb` are collinear
`thereforehataxxhatb=0:{:|(hati,hatj,hatk),(2,-3,4),(3,lambda,mu):|=0`
`(-3mu-4lambda)hati-(2mu-12)hatj+(2lambda+9)hatk=0`
Equating the coefficient of `hati,hatj` and `hatk` on both side we have `2mu-12=0 therefore mu=6`
`2lambda+9=0rArr lambda=-(9)/(2)`
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