Angle between planes - class-XI
Description: angle between planes | |
Number of Questions: 45 | |
Created by: Arav Srivastava | |
Tags: vectors, lines and planes product of vectors maths three dimensional geometry applications of vector algebra the plane three dimensional geometry - ii |
Find the planes bisecting the acute angle between the planes $x-y+2x+1=0$ and $2x+y+z+2=0$
The planes $x-3y+4z-1=0$ and $kx-4y+3z-5=0$ are perpendicular then value of $k$ is
The equation of the plane which bisects the angle between the planes $3x-6y+2z+5=0$ and $4x-12y+3z-3=0$ which contains the origin is ?
The corner of a square OPQR is folded up so that the plane OPQ is perpendicular to the plane OQR, the angle between OP and QR is
The angle between the plane passing through the points $A(0,\ 0,\ 0),\ B(1,\ 1,\ 1),\ C(3,\ 2,\ 1)$ & the plane passing through $A(0,\ 0,\ 0),\ B(1,\ 1,\ 1),\ D(3,\ 1,\ 2)$ is
The angle between the planes
$\vec{r}(\hat{i}+2\hat{j}+\hat{k})=4$ and $\vec{r}(\hat{-i}+\hat{j}+2\hat{k})=9$
What is the cosine of angle between the planes $x + y + z + I = 0$ and $2x-2y+2x+I=0$ ?
The angle between the planes $2x-3y-6z=5$ and $6x+2y-9z=4$ is
A line lies in $YZ-$plane and makes angle of $30^o$ with the $Y-$axis, then its inclination to the $Z-$axis is
If vectors $\bar{b}=\left(\tan\alpha, -1 2\sqrt{\sin \dfrac{\alpha}{2}}\right)$ and $\bar{c}=\left(\tan \alpha , \tan\alpha -\dfrac{3}{\sqrt{\sin \alpha/2}}\right)$ are orthogonal and vector $\bar{a}=(1, 3, \sin 2\alpha)$ make an obtuse angle with the z-axis, then?
Let $\overrightarrow{A}$ be vector parallel to the line of intersection of planes ${p} _{1}$ and ${p} _{2}$ through the origin. ${p} _{1}$ is parallel to the vectors $\overrightarrow{a}=2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=4\hat{j}-3\hat{k}$ and ${p} _{2}$ is parallel to the vectors $\overrightarrow{c}=\hat{j}-\hat{k}$ and $\overrightarrow{d}=3\hat{i}+3\hat{j}$. The angle between $\overrightarrow{A}$ and $2\hat{i}+\hat{j}-2\hat{k}$ is
Let $\overrightarrow{A}$ be vector parallel to the line of intersection of planes ${p} _{1}$ and ${p} _{2}$ through the origin. ${p} _{1}$ is parallel to the vectors $\overrightarrow{a}=2\hat{j}+3\hat{k}$ and $\overrightarrow{b}=4\hat{j}-3\hat{k}$ and ${p} _{2}$ is parallel to the vectors $\overrightarrow{c}=\hat{j}-\hat{k}$ and $\overrightarrow{d}=3\hat{i}+3\hat{j}$. The angle between $\overrightarrow{A}$ and $2\hat{i}+\hat{j}-2\hat{k}$ is:
Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ are such that $\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left(\overrightarrow{c}\times \overrightarrow{d}\right)=0$.Let ${p} _{1}$ and ${p} _{2}$ be the planes determined by the pairs of vectors $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c},\overrightarrow{d}$ respectively . The angle between the planes ${p} _{1}$ and ${p} _{2}$ is
The equation of the bisector of the obtuse angle between the planes $3x+4y-5z+1=0, 5x+12y-13z=0$ is
The equations of the plane which passes through $(0, 0, 0)$ and which is equally inclined to the planes $x-y+z-3=0$ and $x+y+z+4=0$ is/are-
The angle between planes $\overline { r } .\left( 2\overline { i } -3\overline { j } +4\overline { k } \right) +11=0$ and $\overline { r } .\left( 3\overline { i } -2\overline { j } -3\overline { k } \right) +27=0$ is
Find the equation of the bisector planes of the angles between the planes $2x - y + 2z + 3 = 0$ and $3x - 2y + 6z + 8 = 0$.
The angle between two planes is equal to
lf the planes $ x+2y-z+5=0,\ 2x-ky+4z+3=0$ are perpendicular, then $ {k} $ is
In the space the equation $by+ cz+ d= 0$ represents a plane perpendicular to the plane:
If the planes $ 2x-y+ \lambda z- 5=0$ and $x+4y+2z- 7= 0$ are perpendicular, then $\lambda=$
If the planes $\vec{r}. (2\widehat{i}- \widehat{j}+ 2\widehat{k})= 4$ and $\vec{r}. (3\widehat{i}+ 2\widehat{j}+\lambda\widehat{k})= 3$ are perpendicular, then $\lambda =$
The angle between the planes, $\vec{r}.(2\widehat{i}- \widehat{j}+\widehat {k})=6$ and $\vec{r}.(\widehat{i}+ \widehat{j}+2\widehat {k})=5$ , is:
The angle between the planes $ 3x-6y+2z+5=0 $ 7 $ 4x-12y+3z=3 $.Which is bisected by the plane
$ 67x-162y+47z+44 = 0 $is the angle which-
A plane$ P _{1}$ has the equation $2x-y+z=4$ and the plane $P _{2}$ has the equation $x+ny+2z=11.$ If the angle between $P _{1}$ and $P _{2}$ is $\pi /3$ then the value (s) of '$n$' is (are)
The angle between the planes $\displaystyle x + y + z = 0$ and $\displaystyle 3x - 4y + 5z = 0$ is
Which of the following planes is equally inclined to the planes $\displaystyle 4x + 3y - 5z = 0$ and $\displaystyle 5x - 12y + 13z = 0$?
The equation of the plane bisecting the acute angle between the planes $\displaystyle x - y + z - 1 = 0$ and $\displaystyle x + y + z = 2$ is
An angle between the plane, x+y+z=5 and the line of intersection of the planes, 3x+4y+z-1=0 and 5x+8y+2z+14=0, is
The angle between the planes $\bar { r } \cdot \bar { n _{ 1 } } =\left| \bar { { d } _{ 1 } } \right| $ and $\bar { r } \cdot \bar { n _{ 2 } } =\left| \bar { { d } _{ 2 } } \right| $
The tetrahedron has vertices $0\left ( 0,0,0 \right ),A\left ( 1,2,1 \right ),B\left ( 2,1,3 \right )$ and $C\left ( -1,1,2 \right )$, then the angle between the faces $OAB$ and $ABC$ will be
Let $A(0,0,0),B(1,1,1),C(3,2,1)$ and $D(3,1,2)$ be four points. The angle between the planes through the points $A,B,C$ and through the points $A,B,D$ is
The angle between two planes $\displaystyle r.n=q$ and $\displaystyle r.n'=q'$ is
The sine of angle formed by the lateral face ADC and plane of the base ABC of the tetrahedron ABCD where $\displaystyle a\equiv (3, -2, 1); B\equiv (3, 1, 5); C\equiv (4, 0, 3)and D\equiv (1, 0, 0)is$
The equation of a plane bisecting the angle between the plane $2x -y + 2z + 3 = 0$ and $3x- 2y + 6z + 8 = 0$ is
Equation of the plane bisecting the acute angle between the planes $x+2y-2z-9=0,\ 3x-4y+12z-26=0$ is
Equation of the plane bisecting the angle between the planes $2x-y+2z+3=0$ and $3x-2y+6z+8=0$
Let two planes $p _{1}:2x-y+z=2$, and $p _{2}:x+2y-z=3$ are given. The equation of the acute angle bisector of planes $P _{1}$ and $P _{2}$ is
Two planes are prependicular to one another. One of them contains vector $\vec{a}, \vec{b}$ and the other contains $\vec{c}, \vec{d}$ then $(\vec{a} \times \vec{b}) . (\vec{c}\times \vec{d}) = $
Tetrahedron has Vertices at $O(0,0,0)$ , $A(1,2, 1)$ , $B(2,1,3)$ , $C(-1,1,2)$ . Then the angle between the faces $OAB$ and $ABC$ will be
Consider the planes $3x-6y+2z+5=0$ and $4x-12y+3z=3$. The plane $67x-162y+47z+44=0$ bisects the angle between the given planes which-
Angle between planes $2x-y+z$ $=$ $6$ and $x+y+2z$ $=$ $7,$ is -
The equation of the plane bisecting the angle between the planes $\displaystyle 3x +4y = 4$ and $\displaystyle 6x - 2y + 3z + 5 = 0$ that contains the origin, is
The equation of the plane bisecting the obtuse angle between the planes $\displaystyle x+y+z= 1$ and $\displaystyle x+2y-4z= 5$ is
Let two planes $p _{1}:2x-y+z=2$, and $p _{2}:x+2y-z=3$ are given. The equation of the bisector of angle of the planes $P _{1}$ and $P _{2}$ which does not contains origin, is