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

Options

A. 1
B. 2
C. 3
D. 4

Answer

A

Explanation

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`