If the planes bar{r} cdot(2 hat{i}-lambda hat | vedclass

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(C) Two planes $\bar{r} \cdot \bar{n}_1 = d_1$ and $\bar{r} \cdot \bar{n}_2 = d_2$ are parallel if their normal vectors $\bar{n}_1$ and $\bar{n}_2$ ar

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$\frac{5}{2}$

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(C) Two planes $\bar{r} \cdot \bar{n}_1 = d_1$ and $\bar{r} \cdot \bar{n}_2 = d_2$ are parallel if their normal vectors $\bar{n}_1$ and $\bar{n}_2$ are proportional.Here,$\bar{n}_1 = 2 \hat{i} - \lambda \hat{j} + \hat{k}$ and $\bar{n}_2 = 4 \hat{i} - \hat{j} + \mu \hat{k}$.Since they are parallel,we have $\frac{2}{4} = \frac{-\lambda}{-1} = \frac{1}{\mu}$.From $\frac{2}{4} = \frac{\lambda}{1}$,we get $\lambda = \frac{1}{2}$.From $\frac{2}{4} = \frac{1}{\mu}$,we get $\mu = 2$.Therefore,$\lambda + \mu = \frac{1}{2} + 2 = \frac{5}{2}$.

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 parallel,then $\lambda+\mu=$

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