Let veca=2hati+3hatj-hatk and vecb=hati-...

Let `veca=2hati+3hatj-hatk` and `vecb=hati-2hatj+3hatk`. Then , the value of `lamda` for which the vector `vecc=lamdahati+hatj+(2lamda-1)hatk` is parallel to the plane containing `veca` and `vecb`. Is

A

`1`

B

`0`

C

`-1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:

B

We are given that `vecc` is parallel to the plane containing `veca` and `vecb`
`impliesvecc_|_(vecaxxvecb)impliesvecc.(vecaxxvecb)=0implies[(veca, vecb, vecc)]=0`
`implies |(2,3,-1),(1,-2,3),(lamda, 1, 2lamda-1)|=0implieslamda=0`

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