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Find the value of lambda so that the vec...

Find the value of `lambda` so that the vectors
`vec(a)=2hat(i)-3hat(j)+hat(k),vec(b)=hat(i)+2hat(j)-3hat(k) a nd vec(c)=hat(j)+lambda hat(k)` are coplanar.

Text Solution

Verified by Experts

The given vectors will be coplanar if `[vec(a)vec(b)vec(c)]=0`.
Now, ` [vec(a)vec(b)vec(c)]=0hArr|(2,-3,1),(1,2,-3),(0,1,lambda)|=0hArr|(0,-7,7),(1,2,-3),(0,1,lambda)|=0 [R_(1)rarrR_(1)-2R_(2)]hArr(-1)(-7lambda-7)=0hArr7lambda + 7 = 0 hArr lambda=-1`.
Hence, the given vectors are coplanar when `lambda=-1`.
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