The vectors `lamdahati+hatj+2hatk,hati+lamdahatj-hatkand2hati-hatj+lamdahatk` are coplanar, if

Options

A. `lamda=-2`
B. `lamda=0`
C. `lamda=1`
D. `lamda=-1`

Answer

A

Explanation

Let `veca=lamdahati+hatj+2hatj,vecb=hati+lamdahatj-hatkandvecc=2hati-hatj+lamdahatk`
`|[lamda,1,2],[1,lamda,-1],[2,-1,lamda]|=0`
`implieslamda(lamda^(2)-1)-1(lamda+2)+2(-1-2lamda)=0`
`implieslamda^(3)-lamda-lamda-2-2-4lamda=0`
`implieslamda^(3)-6lamda-4=0`
`implies(lamda+2)(lamda^(2)-2lamda-2)=0`
`implieslamda=-2orlamda=(2+-sqrt12)/(2)`
`implieslamda=-2orlamda(2+-2sqrt3)/(2)=1+-sqrt3`