1.

If three vectors 2hat(i)-hat(j)-hat(k), hat(i)+2hat(j)-3hat(k) and 3hat(i)+lambda hat(j)+5hat(k) are coplanar, then the value of lambda is

Answer»

`-4`
`-2`
`-1`
`-8`

Solution :Let`a=2 hati-hatj-hatk, `
`b=hati+2hatj-3hatkand c=3 hati+lamdahatj+5 hatk`
It these vectors are COPLANAR, then [a b c] =0
`implies|{:(2,-1,-1),(1,2,-3),(3, LAMDA,5):}|=0`
`implies2(10+3 lamda)+(5+9)-(lamda-6)=0`
`=20+6 lamda+14-lamda +6=0`
`implies5 lamda +40=0 implies lamda=-8`


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