Exercise

The vector equation of the line passing through the point $(-1,5,4)$ and perpendicular to the plane $z=0$ is 

If the plane $x-3y+5z=\lambda$ passes through the point $(1,2,4)$ then the intercepts on the axes are

The vector equation of planes parallel to $yz-$plane and at a distance $5$ units from origin is 

Find the equation of the plane that meets the coordinate axes at $A, B$ and $C$ respectively such that the centroid of $△ABC$ is $(1, -2, 3)$.

The equation of the plane passing through the intersection of the planes $x+2y+3z+4=0 \text{and} 4x+3y+2z+1=0$ and the origin is

The vector equation of plane passing through the point $(1,1,1)$ and parallel to the plane $\overrightarrow{r}·(2\hat{i}-\hat{j}+2\hat{k})=5$ is 

If the planes $2x-4y+3z=5\text{ and }x+2y+\lambda z=12$ are perpendicular to each other, then $\lambda =$

Angle between the planes $\overrightarrow{r}(2\hat{i}+\hat{j}-\hat{k})=3$ and $\overrightarrow{r}(\hat{i}+2\hat{j}+\hat{k})=1$ is $k$, then $k=$