JEE Exam > JEE Questions > The angle between the line (x + 1)/3 = (y - 1...
Start Learning for Free
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 is
- a)sin-1(-4/√406)
- b)cos⁻1(-4/√406)
- c)sin-1(-2/√406)
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the p...
Line Equation and Plane Equation:
The equation of the line is given by (x + 1)/3 = (y - 1)/2 = (z - 2)/4.
The equation of the plane is given by 2x + y - 3z + 4 = 0.
Angle between Line and Plane:
To find the angle between the line and the plane, we need to find the direction ratios of the line and the normal vector of the plane.
The direction ratios of the line are 3, 2, and 4. Therefore, the direction vector of the line is (3, 2, 4).
The coefficients of x, y, and z in the equation of the plane give us the normal vector to the plane, which is (2, 1, -3).
Angle Calculation:
The angle between the line and the plane can be found using the dot product formula:
cosθ = (a · b) / (|a| * |b|),
where a and b are the direction vector of the line and the normal vector of the plane, respectively.
Substituting the values, we get:
cosθ = (3*2 + 2*1 + 4*(-3)) / (√(3^2 + 2^2 + 4^2) * √(2^2 + 1^2 + (-3)^2)),
cosθ = (-4) / (√(29) * √(14)).
Therefore, the angle between the line and the plane is cos⁻¹(-4/√(406)), which is not provided as an option. Hence, the correct answer is option 'D'.
The equation of the line is given by (x + 1)/3 = (y - 1)/2 = (z - 2)/4.
The equation of the plane is given by 2x + y - 3z + 4 = 0.
Angle between Line and Plane:
To find the angle between the line and the plane, we need to find the direction ratios of the line and the normal vector of the plane.
The direction ratios of the line are 3, 2, and 4. Therefore, the direction vector of the line is (3, 2, 4).
The coefficients of x, y, and z in the equation of the plane give us the normal vector to the plane, which is (2, 1, -3).
Angle Calculation:
The angle between the line and the plane can be found using the dot product formula:
cosθ = (a · b) / (|a| * |b|),
where a and b are the direction vector of the line and the normal vector of the plane, respectively.
Substituting the values, we get:
cosθ = (3*2 + 2*1 + 4*(-3)) / (√(3^2 + 2^2 + 4^2) * √(2^2 + 1^2 + (-3)^2)),
cosθ = (-4) / (√(29) * √(14)).
Therefore, the angle between the line and the plane is cos⁻¹(-4/√(406)), which is not provided as an option. Hence, the correct answer is option 'D'.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The angle between the line (x + 1)/3 = (y - 1)/2 = (z - 2)/4 and the plane 2x + y - 3z + 4 = 0 isa)sin-1(-4/√406)b)cos1(-4/√406)c)sin-1(-2/√406)d)none of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup