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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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Answer» 1 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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