Question:
Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.
Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane.
Updated On: Sep 20, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
The equation of the plane ZOX is y=0
Any plane parallel to it is of the form, y=a
Since, the y-intercept of the plane is 3,
∴ a=3
Thus, the equation of the required plane is y=3.
Was this answer helpful?
0
0
Top Questions on Three Dimensional Geometry
- A straight line drawn from the point P(1,3, 2), parallel to the line \(\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}\), intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE ?
- JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- Let y ∈ R be such that the lines \(L_1:\frac{x+11}{1}=\frac{y+21}{2}=\frac{z+29}{3}\) and \(L_2:\frac{x+16}{3}=\frac{y+11}{2}=\frac{z+4}{\gamma}\) intersect. Let R1 be the point of intersection of L1 and L2. Let O = (0, 0 ,0), and \(\hat{n}\) denote a unit normal vector to the plane containing both the lines L1 and L2.
Match each entry in List-I to the correct entry in List-II.The correct option isList - I List - II (P) γ equals (1) \(-\hat{i}-\hat{j}+\hat{k}\) (Q) A possible choice for \(\hat{n}\) is (2) \(\sqrt{\frac{3}{2}}\) (R) \(\overrightarrow{OR_1}\) equals (3) 1 (S) A possible value of \(\overrightarrow{OR_1}.\hat{n}\) is (4) \(\frac{1}{\sqrt6}\hat{i}-\frac{2}{\sqrt6}\hat{j}+\frac{1}{\sqrt6}\hat{k}\) (5) \(\sqrt{\frac{2}{3}}\) - JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- Let R3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2 ,7). Let
dist(X, Y) denote the distance between two points X and Y in R3. Let
\(S=\left\{X\in\R^3:(dist(X,P)^2)-(dist(X,Q))^2=50\right\}\ and\)
\(T=\left\{Y\in \R^3:(dist(Y,Q))^2-(dist(Y,P))^2=50\right\}\)
Then which of the following statements is (are) TRUE ?- JEE Advanced - 2024
- Mathematics
- Three Dimensional Geometry
- If the foot is perpendicular from (1, 2, 3) to the line \(\frac{x+1}{2} = \frac{y-2}{5} = \frac{z-1}{1}\) is \(( a, \beta, \gamma)\), then find \(a + \beta + \gamma\)
- JEE Main - 2024
- Mathematics
- Three Dimensional Geometry
Let \(\alpha x+\beta y+y z=1\) be the equation of a plane passing through the point\((3,-2,5)\)and perpendicular to the line joining the points \((1,2,3)\) and \((-2,3,5)\) Then the value of \(\alpha \beta y\)is equal to ____
- JEE Main - 2023
- Mathematics
- Three Dimensional Geometry
View More Questions
Questions Asked in CBSE CLASS XII exam
- Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)
- For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?
- Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)
What is the Planning Process?
- CBSE CLASS XII - 2023
- Planning process steps
- Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)
View More Questions
Notes on Three Dimensional Geometry
- Angle Between Two Planes Mathematics
- Analytical Geometry Mathematics
- NCERT Solutions for class 12 Mathematics chapter 11 Three Dimensional Geometry
- Geometry Mathematics
- NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11 1
- NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11 2
Concepts Used:
Plane
A surface comprising all the straight lines that join any two points lying on it is called a plane in geometry. A plane is defined through any of the following uniquely:
- Using three non-collinear points
- Using a point and a line not on that line
- Using two distinct intersecting lines
- Using two separate parallel lines
Properties of a Plane:
- In a three-dimensional space, if there are two different planes than they are either parallel to each other or intersecting in a line.
- A line could be parallel to a plane, intersects the plane at a single point or is existing in the plane.
- If there are two different lines that are perpendicular to the same plane then they must be parallel to each other.
- If there are two separate planes which are perpendicular to the same line then they must be parallel to each other.