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The volume of the tetrahedron having the edges hati+2hatj-hatk, hati+hatj+hatk, hati-hatj+lambdahatk as coterminous, is (2)/(3) cu unit. Then, lambda equals

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Solution :Let `a=hat(i)+2hat(J)-hat(k),b=hat(i)+hat(j)+hat(k) and c=hat(i)-hat(j)+lambdahat(k)`
Since , volume of TETRAHEDRON `=(1)/(6)[abc]`
`rArr(2)/(3)=(1)/(6)|{:(1,2,-1),(1,1,1),(1,-1,lambda):}|`
`rArr (2)/(3)=(1)/(6)[ 1(lambda+1)-2(lambda-1)-1(-1-1)]`
`rArr 4=[-lambda+5]`
`rArr lambda=1`


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