### Equation of a plane in intercept form - class-XII

Description: equation of a plane in intercept form | |

Number of Questions: 34 | |

Created by: Garima Pandit | |

Tags: applications of vector algebra the plane three dimensional geometry - ii three dimensional geometry maths |

The intercepts of the plane $2x-3y+5z-30=0$ are

If $A=(3,1,-2) , B=(-1,0,1)$ and $l, m$ are the projections of AB on the y-axis, zx plane respectively then $3l^2-m+1$=

A plane $

\pi

$ makes intercept 3 and 4 respectively on z-axis and x-axis. If $

\pi

$ is parallel to y-axis, then its equation is

The lengths of the intercepts on the co-ordinate axes made by the plane $5x+2y+z-13=0$ are

Equation of a plane making X-intercept $4$, Y-intercept ($-6$), Z-intercept $3$ is _______.

Two system of rectangular axes have the same origin. If a plane cuts them at distances, $a$, $b$, $c$ and ${a} _{1}$,${b} _{1}$ , ${c} _{1}$ from the origin, then

A plane $x-3y+5z=d$ passes through the point $(1,2,4)$. Intercepts on the axes are

From the point $P(a, b, c)$, let perpendiculars $PL$ and $PM$ be drawn to $YOZ$ and $ZOX$ planes, respectively. Then the equation of the plane $OLM$ is-

If the intercepts made on the axes by the plane which bisects the line joining the points $(1, 2, 3)$ and $(-3, 4, 5)$ at right angles are $(a,0,0), (0,b,0)$ and $(0,0,c)$ then $(a,b,c)$ is

A plane makes intercept $3$ and $4$ with $x$ and $z$ axes and parallel to y-axis is

If from the point $P(f, g, h)$ perpendiculars $PL$ and $PM$ be drawn to $yz$ and $zx$ planes, then equation to the plane $OLM$ is

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

If from the point $P(f,g,h)$ perpendiculars $PL, PM$ be drawn to $yz$ and $zx$ planes, then the equation to the plane $OLM$ is

A plane meet the co-ordinates axes in $A,B,C$ such that the centroid of triangle $ABC$ is the point $\alpha,\beta,\gamma.$ If the equation of the plane be $\displaystyle \frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=k$ then,$k=?$

If a plane meets the coordinate axes in A, B and C such that the centroid of $\Delta ABC$ is $(1, 2, 4)$, then the equation of the plane is?

The equation of a plane passing through the point $A(2, -3, 7)$ and making equal intercepts on the axes, is?

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is $\dfrac{1}{2}$. Then, the plane passes through the point

The equation of the plane which makes with the coordinate axes, a triangle with centroid $(\alpha, \beta, \gamma)$ is given by?

The intercepts made by the plane $\vec{r}\cdot (2\hat{i}-3\hat{j}+4\hat{k})=12$ are?

From a point $P\left ( a,\, b,\, c \right )$ perpendiculars $PM$ and $PN$ are drawn to $zx$ and $xy$-planes respectively, $O$ is the origin. An equation of the plane $OMN$ is

A variable plane moves so that the sum of reciprocals of its intercepts on the three coordinate axes is constant $\lambda$. It passes through a fixed point, which has coordinates

A plane meets the coordinate axes in $A, B, C$ such that the centroid of the triangle $ABC$ is the point $(1,\, r,\, r^2)$. The plane passes through the point $(4, 8, 15)$, if $r$ is equal to

If from the point $P(f, g, h)$ perpendiculars $PL, PM$ be drawn to $yz$ and $zx$ planes then the equation to the plane $OLM$ is -

If $5, 3, 2$ are the direction ratios of a normal to the plane passing through the point $(2, 3, 1)$, then the sum of the intercepts made by the plane on the $x$ -axis and $y$ - axis is

Equation of the plane whose intercepts are $1,2,3$ is

$5, 7$ are the intercepts of a plane on the $y$ - axis, $z$ - axis respectively. If the plane is parallel to the $x$-axis, then the equation of that plane is

The sum of the intercepts of the plane which bisects the line segment joining $(0,1,2)$ and $(2,3,0)$ perpendicularly is

lf a plane meets the coordinate axes at $A,B,C$ , then equation of plane is such that centroid of triangle $ABC$ is $\left (\displaystyle \dfrac{1}{3}\dfrac{2} {3},\dfrac{4}{3}\right)$

If from a point $P(a,b,c)$ perpendicular $PA$ and $PB$ are drawn to $yz$ and $zx$ planes, find the equation of the plane $OAB$:

The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is :

The expression of $x+y+z=1$ in form of $x\cos { \alpha } +y\cos { \beta } +z\cos { \gamma } =p$ is _______.

The sum of Y and Z intercepts of the plane $3x+4y-6z=12$ is ___________.

The plane $ax+by+cz=1$ meets the coordinate axes in $A, B$ and $C$. The centroid of the triangle is:

If a plane passes through a fixed point $\left ( 2, 3, 4 \right )$ and meets the axes of reference in $A$, $B$ and $C$, the point of intersection of the planes through $A$, $B$, $C$ parallel to the coordinate planes can be