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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 |
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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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