Family of Planes

Q. The equation of a plane passing through $\overline{r}.(\hat{i}+\hat{j}+\hat{k})=1$ and $\overline{r}.(2\hat{i}+\hat{k})=2$ can be given by

1. $\overline{r}.\left(\right(1+2\lambda )\hat{i}+\hat{j}+(1+\lambda \left)\hat{k}\right)=1+2\lambda$
2. $\overline{r}.\left(\right(\lambda +2)\hat{i}+\lambda \hat{j}+(\lambda +1\left)\hat{k}\right)=\lambda +2$
3. $\overline{r}.\left(\right(3\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k})=3)=3\lambda$
4. $\overline{r}.(\hat{i}+\hat{j}+\hat{k})=1$

Q. 2 planes can intersect in which of the following ways

1. Point
2. Line
3. Plane
4. Do not intersect at all

Q. 2 planes can intersect in which of the following ways

1. Point
2. Line
3. Plane
4. Do not intersect at all

Q. A plane passing through the intersection of 2 planes $\overline{r}.\overline{n_1}=d_1$ and $\overline{r}.\overline{n_2}=d_2$ can be given by
$\overline{r}.(\overline{n_1}+\lambda \overline{n_1})=d_1+\lambda d_2$

1. True
2. False