If the planes $\bar{r} \cdot(2 \hat{i}-\lambda \hat{j}+\hat{k})=3$ and $\bar{r} \cdot(4 \hat{i}-\hat{j}+\mu…
If the planes $\bar{r} \cdot(2 \hat{i}-\lambda \hat{j}+\hat{k})=3$ and $\bar{r} \cdot(4 \hat{i}-\hat{j}+\mu \hat{k})=5$ are paralle, then values of $\lambda$ and $\mu$ are respectively
$\frac{1}{2}, 2$
$\frac{-1}{2}, 2$
$\frac{1}{2},-2$
$\frac{-1}{2},-2$
Solution
The two planes are parallel hence
$\begin{aligned}
& \frac{2}{4}=\frac{-\lambda}{-1}=\frac{1}{\mu} \\
& \Rightarrow \lambda=\frac{1}{2} \text { and } \mu=2
\end{aligned}$