Explore Exams
Login Signup
Sign in Open App
JEE Exam  >  JEE Test  >  Mathematics (Maths) Main & Advanced  >  Test: Intercept Form And Family Of Planes - JEE MCQ

Intercept Form And Family Of Planes - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Intercept Form And Family Of Planes (5 Questions)

You can prepare effectively for JEE Mathematics (Maths) for JEE Main & Advanced with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Intercept Form And Family Of Planes". These 5 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 5

Sign up on EduRev for free to attempt this test and track your preparation progress.

Test: Intercept Form And Family Of Planes - Question 1
Save

The equation of plane through the intersection of planes (x+y+z =1) and (2x +3y – z+4) =0 is​

Detailed Solution: Question 1

The equation of any plane passing through the line of intersection of two planes

As we have learnt from the concept Equation of plane 

Test: Intercept Form And Family Of Planes - Question 2
Save

The equation of the plane passing through the line of intersection of the planes x-2y+3z+8=0 and 2x-7y+4z-3=0 and the point (3, 1, -2) is:​

Detailed Solution: Question 2

(x - 2y + 3z + 8) + μ(2x - 7y + 4z - 3) = 0
i.e, (1 + 2μ)x - (2 + 7μ)y + (3 + 4μ)z + (8 - 3μ) = 0......(1)
 the required plane is passing through (3, 1, -2)
so, 3(1 + 2μ) - (1)(2 + 7μ) + (-2)(3 + 4μ)+ (8 - 3μ) = 0
3 + 6μ - 2 - 7μ -6 -8μ + 8 - 3μ = 0
by solving, μ = 1/4
putting μ in equation (1)
we get the required equation of plane as :- 6x - 15y + 16z + 29 = 0

Clear all your doubts with EduRev
Test: Intercept Form And Family Of Planes - Question 3
Save

If  are the equations of two given lines the, what is the condition for coplanarity of the twi lines in the vector form.

Test: Intercept Form And Family Of Planes - Question 4
Save

The equation of the plane which makes the intercepts 3, 4, 12 with X-axis, Y-axis and Z-axis respectively is:​

Detailed Solution: Question 4

To find the equation of a plane with intercepts of 3, 4, and 12 on the X, Y, and Z axes respectively:

- The equation of a plane in intercept form is x/a + y/b + z/c = 1, where a, b, and c are the intercepts on the axes.
- Substituting the given intercepts, we get x/3 + y/4 + z/12 = 1.
- Multiplying by 12 to clear the fractions, we get 4x + 3y + z = 12.
- Therefore, the correct answer is B: 4x + 3y + z = 12.

Test: Intercept Form And Family Of Planes - Question 5
Save

The equation of the plane passing through the intersection of the planes  and and the point (1, 2, 1) is:​

Detailed Solution: Question 5

n1 = 2i + j + k
n2 = 2i + 3j - 4k
p1 = 4,   p2 = -6
r.(n1 + λn2) = p1 + λp2
=> r . [2i + j + k + λ(2i + 3j - 4k)] = 4 - 6λ
=> r . [ i(2 + 2λ) + j(1 + 3λ) + k(1 - 4k)] = 4 - 6λ
Taking r = xi + yj + zk
(2 + 2λ)x + (1 + 3λ)y + (1 - 4k)z = 4 - 6λ
(2x + y + - z - 4) + λ(2x + 3y - 4k + 6) = 0
Given points are (1,2,1) 
(2 + 2 - 1 - 4) + λ(2 + 6 - 4 + 6) = 0
-1 + λ(10) = 0
 λ = 1/10
Substitute  λ = 1/10, we get
18x + 7y + 14z - 46=0

173 videos|510 docs|140 tests
Join Course
Information about Test: Intercept Form And Family Of Planes Page
In this test you can find the Exam questions for Test: Intercept Form And Family Of Planes solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Intercept Form And Family Of Planes, EduRev gives you an ample number of Online tests for practice
Download as PDF

About this JEE Practice Test

This test contains 5 MCQs on Intercept Form And Family Of Planes with detailed solutions for each question. It is part of the Mathematics (Maths) for JEE Main & Advanced course on EduRev, designed to align with the current JEE syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

Explore more JEE Study Resources

If you found this Intercept Form And Family Of Planes MCQ Test helpful, you can further enhance your JEE preparation with in-depth courses on EduRev, for all the subjects and topics available in Mathematics (Maths) for JEE Main & Advanced course. The course offers:
  • Video Lectures: covering all the topics of Mathematics (Maths) for JEE Main & Advanced
  • Notes for Revision: offering revision notes, important questions, summaries, flashcards, cheatsheets & more for JEE preparation
  • MCQ Test: variety of questions as per the pattern of JEE exam
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup