If the vectors a= i- j+2 k, b=2 i+4 j+ k and c= i+ j+ k are mutually orthogonal, then (,)=

Question

If the vectors $\vec a=\hat i-\hat j+2\hat k$, $\vec b=2\hat i+4\hat j+\hat k$ and $\vec c=\lambda\hat i+\hat j+\mu\hat k$ are mutually orthogonal, then $(\lambda,\mu)=$

Accepted Answer

$\vec b\cdot\vec c=0 \implies 2\lambda+4+\mu=0$ \ldots (i); $\vec c\cdot\vec a=0 \implies \lambda-1+2\mu=0$ \ldots (ii)

Solving: $\lambda=-3$, $\mu=2$

Solutions · 1