Lines in space - class-XII
Description: lines in space | |
Number of Questions: 31 | |
Created by: Vinaya Modi | |
Tags: maths product of vectors vectors:planes in three dimensions vectors, lines and planes applications of vector algebra the plane three dimensional geometry - ii three dimensional geometry |
The cartesian equation of the plane which is at a distance of 10 unite from the original and perpendicular to the vector i + 2j -2k is
The equation of the plane through the point $(0, -1, -6)$ and $(-2, 9, 3)$ are perpendicular to the plane $x-4y-2z=8$ is
The normal form of $2x-2y+z=5$ is
If a line is given by $\dfrac{x-2}3 = \dfrac{y+10}5 = \dfrac{z+6}2$, then which of the following points lies on this line?
Vector form of plane $2x-z+1=0$ is _________
Find the equation of the plane through the points $(1, 0, -1), (3, 2, 2)$ and parallel to the line $\dfrac{x-1}{1}=\dfrac{y-1}{-2}=\dfrac{z-2}{3}$.
The equation of the plane passing through the straight line $\dfrac{x-1}{2}=\dfrac{y+1}{-1}=\dfrac{z-3}{4}$ and perpendicular to plane $x+2y +z=12$ is:
Equation of the plane containing the straight lines $\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4}$ and perpendicular to the plane containing the straight lines $\dfrac{x}{3} = \dfrac{y}{4} = \dfrac{z}{2}$ and $\dfrac{x}{4} = \dfrac{y}{2} = \dfrac{z}{3}$
Let a,b,c be any real numbers.Suppose that there are real numbers x,y,z not all zero such that $x=cy+bz , y=az+cx$ and $z=bx+ay$, then ${a^2} + {b^2} + {c^2} + 2abc $ is equal to
The direction cosines of the normal to the plane $x+2y-3z+4=0$ are
The Cartesian equation of the plane $\vec r=(1+\lambda-\mu)\hat i+(2-\lambda)\hat j+(3-2\lambda+2\mu)\hat k$ is-
The equation of a plane which passes through the point of intersection of lines $\dfrac {x-1}{3}=\dfrac {y-2}{1}=\dfrac {z-3}{2}$, and $\dfrac {x-3}{1}=\dfrac {y-1}{2}=\dfrac {z-2}{3}$ and at greatest distance from point $(0, 0, 0)$ is-
Let $A (1, 1, 1), B(2, 3, 5)$ and $C(-1, 0, 2)$ be three points, then equation of a plane parallel to the plane $ABC$ and at the distance $2$ is
The plane which passes through the point $(3, 2, 0)$ and the line $\dfrac {x-3}{1}=\dfrac {y-6}{5}=\dfrac {z-4}{4}$ is:
Equation of the plane passing through the points $(2, 2, 1)$ and $(9, 3, 6)$, and perpendicular to the plane $2x+6y+6z-1=0$ is-
The cartesian equation of the plane $\overrightarrow { r } =\left( 1+\lambda -\mu \right) i+\left( 2-\lambda \right) j+\left( 3-2\lambda +2\mu \right) k$ is:
If $lx+my+nz=p$ is equation of plane in normal form, then :
The equation of the plane through the points $(2,3,1)$ and $(4,-5,3)$ and parallel to $x$-axis is
Equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to each of the planes $x+ 2y+ 3z= 7$ and $2x- 3y +4z= 0$, is
The cartesian form of the plane
$ { r } =(s-2t)\hat { i+(3-t)\hat { j+(2s+t)\hat { k } } } $ is
The general equation of plane which is parallel to x-axis is
Equation of plane through $(2, 1,4)$ and having $\mathrm{d}.\mathrm{c}$'s of its normal $\alpha,\ \beta,\ \gamma$ is
If the equation of the plane passing through the points $(1,2,3)$, $(-1,2,0)$ and perpendicular to the $zx$ - plane is $ax + by + cz + d$ $=$ $ 0$ $(a>0)$, then
A plane $\Pi$ passes through the point $(1,1,1)$. If $b,c, a$ are the direction ratios of a normal to the plane, where $a, b, c (a<b<c)$ are the prime factors of $2001$, then the equation of the plane $\pi$ is
The equation of the plane passing through the origin and containing the lines whose d.cs are proportional to $1,-2,2$ and $2,3,-1$ is:
The vector equation of the plane passing through the planes $r.(i+j+k)=6$ and $r.(2i+3j+4k)=-5$ and the point $(1,1,1)$ is
The cartesian equation of plane $\bar{r}.(2, -3, 4) = 5$ is _____
The equation(s) of the plane, which is/are equally inclined to the lines $\dfrac {x-1}{2}=\dfrac {y}{-2}=\dfrac {z+2}{-1}$ and $\dfrac {x+3}{8}=\dfrac {y-4}{1}=\dfrac {z}{-4}$ and passing through the origin is/are
A plane through the line $\displaystyle \frac{x - 1}{1} = \frac{y + 1}{-2} = \frac{z}{1}$ has the equation
Equation of a plane through the line $\displaystyle \frac{x\, -\, 1}{2}= \frac{y\, -\, 2}{3}= \frac{z\, -\, 3}{4}$ and parallel to a coordinate axis is