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A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:
- a)( √2 , -1, 4 )
- b)( - √2 , -1, -4 )
- c)( - √2 ,1, -4 )
- d)( √2 ,1, 4 )
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and makin...
is the equation of plane ……(1)y - z = 0 ..........(2)
So plane equation is
Check options ( √2,1, 4 ) satisfies second equation
Most Upvoted Answer
A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and makin...
To determine the equation of the plane passing through the given points, we first need to find the normal vector of the plane. The normal vector will be perpendicular to the plane.
Let's call the two given points A and B.
Point A: (0, -1, 0)
Point B: (0, 0, 1)
To find the normal vector, we can take the cross product of the vectors AB and a vector in the direction of the line of intersection between the plane and the xy-plane.
Vector AB = B - A = (0, 0, 1) - (0, -1, 0) = (0, 1, 1)
A vector in the direction of the line of intersection between the plane and the xy-plane can be taken as the z-axis vector, which is (0, 0, 1).
Now, taking the cross product of AB and the z-axis vector:
(0, 1, 1) x (0, 0, 1) = (1, 0, 0)
So, the normal vector to the plane is (1, 0, 0).
Now, let's find the equation of the plane using the normal vector and one of the given points (A).
The equation of a plane can be written in the form Ax + By + Cz = D, where (A, B, C) is the normal vector and (x, y, z) is a point on the plane.
Substituting the values, we have:
1(x - 0) + 0(y + 1) + 0(z - 0) = 0
x + 0 + 0 = 0
x = 0
Therefore, the equation of the plane passing through the given points is x = 0.
Let's call the two given points A and B.
Point A: (0, -1, 0)
Point B: (0, 0, 1)
To find the normal vector, we can take the cross product of the vectors AB and a vector in the direction of the line of intersection between the plane and the xy-plane.
Vector AB = B - A = (0, 0, 1) - (0, -1, 0) = (0, 1, 1)
A vector in the direction of the line of intersection between the plane and the xy-plane can be taken as the z-axis vector, which is (0, 0, 1).
Now, taking the cross product of AB and the z-axis vector:
(0, 1, 1) x (0, 0, 1) = (1, 0, 0)
So, the normal vector to the plane is (1, 0, 0).
Now, let's find the equation of the plane using the normal vector and one of the given points (A).
The equation of a plane can be written in the form Ax + By + Cz = D, where (A, B, C) is the normal vector and (x, y, z) is a point on the plane.
Substituting the values, we have:
1(x - 0) + 0(y + 1) + 0(z - 0) = 0
x + 0 + 0 = 0
x = 0
Therefore, the equation of the plane passing through the given points is x = 0.
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A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct answer is option 'D'. Can you explain this answer?
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A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct 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 A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct 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 A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct answer is option 'D'. Can you explain this answer?.
A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct 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 A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct 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 A plane passing through the points ( 0, -1, 0) and ( 0, 0,1) and making an angle π/4 with the plane y - z + 5 = 0 , also passes through the point:a)( √2 , -1, 4 )b)( - √2 , -1, -4 )c)( - √2 ,1, -4 )d)( √2 ,1, 4 )Correct answer is option 'D'. Can you explain this answer?.
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