Equation of Plane

The equation of the plane whose intercepts on the coordinate axes are $2,-4$ and $5$ respectively is

The intercepts cut off by the plane $2x+y-z=5$ are

A non-zero vector $\overrightarrow{a}$ is parallel to the line of intersection of the plane determined by the vectors $\hat{i}$, $\hat{i}+\hat{j}$ and the plane determined by the vectors $\hat{i}-\hat{\mathrm{j}}, \hat{i}+\hat{k}$. The angle between $\overrightarrow{a}$ and $\hat{i}-2\hat{j}+2\hat{k}$ is :-

The equation of the plane passing through the points $(a, 0, 0), (0, b, 0)$ and $\left(0, 0, c\right)$ is

If a plane has the intercepts $a,b,c$ and it is at a distance of $p$ from the origin, then

The equation of the plane passing through the points $(2,5,-3),(-2,-3,5)$ and $(5,3,-3)$ is

P is a fixed point $\left(a,\mathrm{ }a,\mathrm{ }a\right)$ on a line through the origin equally inclined to the axes, then any plane through P perpendicular to $OP$ , makes intercepts on the axes, the sum of whose reciprocals is equal to

If a plane passes through the point $\left(\mathrm{1,1},1\right)$ and is perpendicular to the line $\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}$ , then its perpendicular distance from the origin is

The distance of the point $\left(-1,\mathrm{ }-5,\mathrm{ }-10\right)$ from the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane $x-y+z=5$ , is

The equation of the plane passing through the points $\left(\mathrm{3,2},2\right)$ and $\left(\mathrm{1,0},-1\right)$ and parallel to the line $\frac{x-1}{2}=\frac{y-1}{-2}=\frac{z-2}{3}$ , is

If for a plane, the intercepts on the coordinate axes are 8, 4, 4 then the length of the perpendicular from the origin on to the plane is

If $O$ be the origin and the co-ordinates of $P$ be $\left(1,\mathrm{ }2,\mathrm{ }-3\right)$ , then the equation of the plane passing through $P$ and perpendicular to $OP$ is

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

The equations $\left|x\right|=p,\left|y\right|=p,\left|z\right|=p$ in $\mathrm{x}\mathrm{y}\mathrm{z}$ space represent

If the plane $x-3y+5z=d$ passes through the point $\left(\mathrm{1,2},4\right)$ , then the lengths of intercepts cut by it on the axes of $x, y, z$ are respectively

If the length of perpendicular drawn from origin on a plane is 7 units and its direction ratios are $-3, 2, 6$ , then that plane is

The equation of a plane which cuts equal intercepts of unit length on the axes, is

The graph of the equation $y^2+z^2=0$ in three dimensional space is

If from a point $\mathrm{ }P\left(a,b,c\right)$ perpendiculars $PA$ and $PB$ are drawn to $yz$ and $zx$ planes, then the equation of the plane $OAB$ is