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Find the value of lambda so that the three vectors are co-planar. hati+2hatj+3hatk, 4hati+hatj+lambdahatk and lambdahati-4hatj+hatk

Answer»

Solution :Let `veca = hati+2hatj+3hatk`
`vecb = 4hati+hatj+lambdahatk`
`VECC = lambdahati-4hatj+hatk`
If the GIVEN vectors are coplanar, then `vecaxxvecb.vecc = 0`

`2lambda^2+11lambda-10lambda-55 = 0`
`IMPLIES lambda(2lambda+11)-5(2lambda+11) = 0`
`implies(lambda-5)(2lambda+11) = 0`
`implies(lambda-5)(2lambda+11) = 0`
`implies lambda = 5` or -11/2


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