The equation of the plane,passing through the intersection of the planes $x+y+z=1$ and $2x+3y-z+4=0$ and parallel to $Y$-axis is

The line of intersection of the planes $\overline{r} \cdot(3 \hat{i}-\hat{j}+\hat{k})=1$ and $\overline{r} \cdot(\hat{i}+4 \hat{j}-2 \hat{k})=2$ is parallel to which of the following vectors?

If the line $\frac{x - 4}{1} = \frac{y - 2}{1} = \frac{z - k}{2}$ lies on the plane $2x - 4y + z = 7$,then $k = . . . . $

The distance of the point $O(\vec{0})$ from the plane $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=5$ measured parallel to the vector $2 \hat{i}+3 \hat{j}-6 \hat{k}$ is:

If the line $\frac{x-3}{2}=\frac{y+2}{-1}=\frac{z+4}{3}$ lies in the plane $\ell x+m y-z=9$,then $\ell^2+m^2$ is

Let $P(3, 2, 6)$ be a point in space and $Q$ be a point on the line $\vec{r} = (\hat{i} - \hat{j} + 2\hat{k}) + \mu(-3\hat{i} + \hat{j} + 5\hat{k})$. For what value of $\mu$ is the vector $\vec{PQ}$ parallel to the plane $x - 4y + 3z = 1$?