If the vectors $\vec a=\hat i-\hat j +2\hat k, \vec b=2\hat i+4\hat j+\hat k$ and $\vec c =λ\hat i+\hat j+μ\hat k$ are mutually orthogonal, then $(λ, μ) =$
Answer & explanation
Correct answer: option 3
We have,
$\vec b.\vec c=0$ and $\vec a.\vec c=0$
$⇒2λ+ 4+μ=0$ and $λ-1 + 2μ = 0$
$⇒2λ+μ+4=0$ and $λ+2μ-1=0$
$⇒λ=-3$ and $μ = 2$