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If a=hati+hatj+hatk, b=2hati+lambda hati+lambdahatj+hatk, c=hati-hatj+4hatk and a.(bxxc)=10 then lambda is equal to

Answer»

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10

Solution :Given, `a=hati,hatj+hatk, b=2hati+lambdahatj+hatk and c=hati-hatj+4hatk`
Also, given `a.(bxxc)=10`
`RIGHTARROW [{:(,1,1,1),(,2,lambda,1),(,1,-1,4):}]=10`
`Rightarrow 1(4lambda+1-1(8-1)+1(-2-lambda)=10`
`Rightarrow 4lambda+1-7-2-lambda=10`
`Rightarrow 3lambda=18`
`Rightarrow lambda=6`


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