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JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Intercept Form And Family Of Planes - JEE MCQ

Test: Intercept Form And Family Of Planes - JEE MCQ


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5 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Intercept Form And Family Of Planes

Test: Intercept Form And Family Of Planes for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Intercept Form And Family Of Planes questions and answers have been prepared according to the JEE exam syllabus.The Test: Intercept Form And Family Of Planes MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Intercept Form And Family Of Planes below.
Solutions of Test: Intercept Form And Family Of Planes questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Intercept Form And Family Of Planes solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Intercept Form And Family Of Planes | 5 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Intercept Form And Family Of Planes - Question 1
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The equation of plane through the intersection of planes (x+y+z =1) and (2x +3y – z+4) =0 is​

Detailed Solution for Test: Intercept Form And Family Of Planes - 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
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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 for Test: Intercept Form And Family Of Planes - 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

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Test: Intercept Form And Family Of Planes - Question 3
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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
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The equation of the plane which makes the intercepts 3, 4, 12 with X-axis, Y-axis and Z-axis respectively is:​
Test: Intercept Form And Family Of Planes - Question 5
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The equation of the plane passing through the intersection of the planes  and and the point (1, 2, 1) is:​
Detailed Solution for Test: Intercept Form And Family Of Planes - 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

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