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If the volume of parallelopiped formed b...

If the volume of parallelopiped formed by the vectors `hati+lamdahatj+hatk,hatj+lamdahatk` and `lamdahati+hatk` is minimum then `lamda` is equal to (1) `-(1)/(sqrt(3))` (2) `(1)/(sqrt(3))` (3) `sqrt(3)` (4)`-sqrt(3)`

A

`-(1)/(sqrt3)`

B

`(1)/(sqrt3)`

C

`-sqrt3`

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
B
`"Volume of 11 pipe "[bara barb barc]=|(1, lambda, 1),(0,1,lambda),(lambda,0,1)|=f(lambda)" (say)"`
`f(x)=1" "lambda^(3)-1=0`
`lambda=pm(1)/(sqrt3)`
`f^(n)(x)=6lambda gt " at "lambda=+(1)/(sqrt3)" "therefore" min if "lambda=(1)/(sqrt3)`
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