1.

If vector hat(i)+hat(j)+hat(k), hat(i)-hat(j)+hat(k) and 2hat(i)+3hat(j)+lambda hat(k) are coplanar, then lambda is equal to

Answer»

`-2`
3
2
`-3`

SOLUTION :SINCE, vectors `hati+hatj+hatk, hati-hatj+hatk" and "2hati+3hatj+lamdahatk` ARECOPLANAR, therefore
`|{:(1,1,1),(1,-1,1),(2,3,lamda):}|=0`
`rArr""2(-lamda-3)-1(lamda-2)+1(3+2)=0`
`rArr""-lamda-3 -lamda+2+5=0`
`rArr""2lamda=4lamda=2`


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