
Find 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.
A. \[3x + 2z = 1\]
B. \[3x + 2z = 6\]
C. \[2x + 3z = 6\]
D. \[3x + 2z = 0\]
Answer
163.2k+ views
Hint: First, consider the equation of plane as \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\]. Then, apply the given condition (parallel to y-axis) and simplify the equation of the plane. After that, substitute the values of the intercepts in the equation of plane and solve it to get the required answer.
Formula Used:The equation of plane: \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\]
Complete step by step solution:Given:
The plane is parallel to the y-axis.
The x-intercept: 2 units
The z-intercept: 3 units
Let consider,
The general equation of a plane is \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\].
It is given that the plane is parallel to the y-axis.
So, substitute \[y = 0\] in the equation of plane.
We get,
\[\dfrac{x}{a} + \dfrac{0}{b} + \dfrac{z}{c} = 1\]
\[ \Rightarrow \dfrac{x}{a} + \dfrac{z}{c} = 1\] \[.....\left( 1 \right)\]
We have, x-intercept: \[a = 2\] and z-intercept: \[c = 3\].
Substitute these values in the equation \[\left( 1 \right)\].
\[\dfrac{x}{2} + \dfrac{z}{3} = 1\]
\[ \Rightarrow \dfrac{{2x + 3z}}{{2 \times 3}} = 1\]
\[ \Rightarrow \dfrac{{2x + 3z}}{6} = 1\]
\[ \Rightarrow 2x + 3z = 6\]
Thus, the equation of the plane is \[2x + 3z = 6\].
Option ‘B’ is correct
Note: Remember the following equations of the plane:
If the plane is parallel to the x-axis: \[by + cz = d\], because \[x = 0\]
If the plane is parallel to the y-axis: \[ax + cz = d\], because \[y = 0\]
If the plane is parallel to the z-axis: \[ax + by = d\], because \[z = 0\]
Formula Used:The equation of plane: \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\]
Complete step by step solution:Given:
The plane is parallel to the y-axis.
The x-intercept: 2 units
The z-intercept: 3 units
Let consider,
The general equation of a plane is \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\].
It is given that the plane is parallel to the y-axis.
So, substitute \[y = 0\] in the equation of plane.
We get,
\[\dfrac{x}{a} + \dfrac{0}{b} + \dfrac{z}{c} = 1\]
\[ \Rightarrow \dfrac{x}{a} + \dfrac{z}{c} = 1\] \[.....\left( 1 \right)\]
We have, x-intercept: \[a = 2\] and z-intercept: \[c = 3\].
Substitute these values in the equation \[\left( 1 \right)\].
\[\dfrac{x}{2} + \dfrac{z}{3} = 1\]
\[ \Rightarrow \dfrac{{2x + 3z}}{{2 \times 3}} = 1\]
\[ \Rightarrow \dfrac{{2x + 3z}}{6} = 1\]
\[ \Rightarrow 2x + 3z = 6\]
Thus, the equation of the plane is \[2x + 3z = 6\].
Option ‘B’ is correct
Note: Remember the following equations of the plane:
If the plane is parallel to the x-axis: \[by + cz = d\], because \[x = 0\]
If the plane is parallel to the y-axis: \[ax + cz = d\], because \[y = 0\]
If the plane is parallel to the z-axis: \[ax + by = d\], because \[z = 0\]
Recently Updated Pages
Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Instantaneous Velocity - Formula based Examples for JEE

JEE Main Chemistry Question Paper with Answer Keys and Solutions

JEE Main Reservation Criteria 2025: SC, ST, EWS, and PwD Candidates

What is Normality in Chemistry?

Chemistry Electronic Configuration of D Block Elements: JEE Main 2025

Other Pages
NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations

NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks
