Angle between a line and a plane - class-XII
Description: angle between a line and a plane | |
Number of Questions: 35 | |
Created by: Amal Dixit | |
Tags: applications of vector algebra three dimensional geometry - ii maths product of vectors |
The angle between the line $\dfrac{x-1}{1}=\dfrac{y+2}{1}=\dfrac{z-4}{0}$ and the plane $y+z+2=0$ is
The angle between the line $\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4}$ and the plane $3x + 2y - 3z = 4$, is
The projection of the line segment joining the points $(1, 2, 3)$ and $(4, 5, 6)$ on the plane $2x + y + z = 1$ is
If $\overline {c}$ is perpendicular to $\overline {a}$ and $\overline {b}$ , $\left| \overline {a} \right| =3,\ \left| \overline {b} \right|=4,\ \left| \overline {c} \right|=5$ and the angle between $\overline {a}$ and $\overline {b}$ is $\dfrac{\pi}{6}$ then $[\overline {a}\ \ \ \overline {b}\ \ \ \overline {c}]=$
An angle between the plane , $x+y+z=5$ and the line of intersection of the planes, $3x+4y+x-1=0$ and $5x+8y+2z+14=0$
Read the following statement carefully and identify the true statement
(a) Two lines parallel to a third line are parallel
(b) Two lines perpendicular to a third line are parallel
(c) Two lines parallel to a plane are parallel
(d) Two lines perpendicular to a plane are parallel
(e) Two lines either intersect or are parallel
The line $\dfrac {x - 2}{3} = \dfrac {y - 3}{4} = \dfrac {z - 4}{5}$ is parallel to the plane.
If the projection of point P$(\vec{p})$ on the plane $\vec{r}\cdot \vec{n}=q$ is the points $S(\vec{s})$, then.
The line $\cfrac{x+3}{3}=\cfrac{y-2}{-2}=\cfrac{z+1}{1}$ and the plane $4x+5y+3z-5=0$ intersect at a point
If $a,b$ and $c$ are three unit vectors equally inclined to each other at angle $\theta$. Then, angle between $a$ and the plane of $b$ and $c$ is
If the line $\cfrac{x-1}{2}=\cfrac{y+3}{1}=\cfrac{z-5}{-1}$ is parallel to the plane $px+3y-z+5=0$, then the value of $p$
The angle between the plane $2 x - y + z = 6$ and a perpendiculars to the planes $x + y + 2 z = 7$ and $x - y = 3$ is
Statement 1: Line $\dfrac {x-1}{1}=\dfrac {y-0}{2}=\dfrac {z+2}{-1}$ lies in the plane $2x-3y-4z-10=0$.
Statement 2: If line $\vec r=\vec a+\lambda \vec b$ lies in the planar $\vec r\cdot \vec c=n$ (where n is scalar), then $\vec b\cdot \vec c=0$.
If $\theta$ denotes the acute angle between the line $\bar{r} = (\bar{i} + 2\bar{j} - \bar{k}) + \lambda (\bar{i} - \bar{j} + \bar{k})$ and the plane $\bar{r} = (2\bar{i} - \bar{j} + \bar{k}) = 4$, then $\sin \theta + \sqrt 2 \cos \theta$
Let $\vec {AB}=\hat {i}-\hat {j}+\hat {k}$ be rotated about $A$ along the plane $3x-y-2z=5$ by an angle $\cos^{-1}\dfrac {\sqrt {2}}{3}$ so that the point $B$ reaches the point $C$, then the vector representing $AC$ may be
Gives the line $\displaystyle L:\frac { x-1 }{ 3 } =\frac { y+1 }{ 2 } =\frac { z-3 }{ -1 } $ and the plane $\pi :x-2y=0$. Of the following assertions, the only one that is always true is:
Consider a plane $x + y - z = 1$ and the point $A(1, 2, -3)$. A line $L$ has the equation $x = 1 + 3r$, $y = 2 - r$, $z = 3 + 4r$
If the angle between the line $x=\dfrac{y-1}{2}=\dfrac{z-3}{\lambda}$ and the plane $x+2y+3z=4$ is $\cos ^{ -1 }{ \left( \sqrt { 5/14 } \right) } $ then $\lambda$=
Consider plane containing line $\dfrac{x+1}{-3} = \dfrac{y-3}{z} = \dfrac{z+2}{-1}$ and passing through the point $(1, -1, 0)$. The angle made by the plane with x-axis is
Consider plane containing line $\dfrac{x+1}{-3} = \dfrac{y-3}{2} = \dfrac{z+2}{-1}$ and passing through the point $(1, -1, 0)$ . The angle made by the plane with x-axis is
If the plane $2x-3y+6z-11=0$ makes an angle $\sin^{-1}(k)$ with x-axis, then $k$ is equal to:
The angle between the line $\displaystyle x = y = z$ and the plane $\displaystyle 4x - 3y + 5z = 2$ is
Given the line $\displaystyle L:\frac { x-1 }{ 3 } =\frac { y+1 }{ 2 } =\frac { z-3 }{ -1 } $ and the plane $\pi :x-2y=0$. Of the following assertion, the only one that is always true is
If the plane $2x - 3y + 6z - 11 = 0$ makes an angle $sin^{-1}(k)$ with x-axis, then k is equal to
Given the line $L:\displaystyle\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1}$ and the plane II:$x-2y-z=0$. Of the following assertions, the only one that is always true, is?
Plane $2x+3y+6z=15=0$ makes angle of measure ________ with Y-axis.
If the angle bwteen a line $x=\dfrac{y-1}{2}=\dfrac{z-3}{\lambda}$ and normal to the plane $x+2y+3z=4$ is $\cos^{-1}{\sqrt{\dfrac{5}{14}}}$, then possible value(s) of $\lambda$ is/are
If the angle between the line $x=\dfrac { y-1 }{ 2 } =\dfrac { z-3 }{ \lambda}$ and the plane $x+2y+3z=4$ is $\cos ^{ -1 }{ \sqrt { \dfrac { 5 }{ 14 } } },$ then $\lambda$ equals:
If the angle between the line $x=\cfrac{y-1}{2}=\cfrac{z-3}{\lambda}$ and the plane $x+2y+3z=4$ is $\cos ^{ -1 }{ \left( \sqrt { \cfrac { 5 }{ 14 } } \right) } $, then $\lambda$ equals:
If the angle between the line $x=\cfrac{y-1}{2}=\cfrac{z-3}{\lambda}$ and the plane $x+2y+3z=4$ is $\cos ^{ -1 }{ \left( \sqrt { \cfrac { 5 }{ 14 } } \right) } $, then $\lambda$ equals
How is the line $\displaystyle \frac{x-4}{4}=\frac{y-12}{12}=\frac{z-8}{8}$ related to the planes
(A) $\displaystyle x-y+z=0$
(B) $\displaystyle x-y+z-6=0$
If the angle $\theta $ between the line $\displaystyle \frac{x+1}{1}=\frac{y-1}{2}=\frac{z-2}{2}$ and the plane $2x-y+\sqrt{\lambda} z+4=0$ is such that $\displaystyle \sin \theta =\frac{1}{3}$, then value of $\lambda $ is
If $\displaystyle \theta$ is the angle between the line
$\vec r=2i+j-k+\left ( i+j+k \right )t$ and the plane
$\displaystyle \vec r\cdot \left ( 3i-4j+5k \right )=q$, then
The projection of line $\displaystyle\frac{x}{2}=\frac{y-1}{2}=\frac{z-1}{1}$ on a plane 'P' is $\displaystyle\frac{x}{1}=\frac{y-1}{1}=\frac{z-1}{-1}$. If the plane P passes through $(k, -2, 0)$, then k is greater than.