Coplanarity
Four points are coplanar if the volume of tetrahedron formed by them is
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More three dimensional geometry Practice Questions
A point divides the segment joining (2, -1, 3) and (4, 3, -1) internally in the ratio 1:3, so find t...
A point divides the segment joining (2, -1, 3) and (4, 3, -1) internally in the ratio 1:3, so find t...
Decide whether the three points (1, 2, 3), (2, 4, 6), and (4, 8, 12) are collinear in three-dimensio...
Decide whether the three points (1, 2, 3), (2, 4, 6), and (4, 8, 12) are collinear in three-dimensio...
Find the radius of the sphere whose equation is x^2 + y^2 + z^2 - 2x + 4y - 6z + 5 = 0 in three-dime...
Find the radius of the sphere whose equation is x^2 + y^2 + z^2 - 2x + 4y - 6z + 5 = 0 in three-dime...
Find the acute angle between the two planes represented by the equations x + y + z = 5 and x - y + 2...
Find the acute angle between the two planes represented by the equations x + y + z = 5 and x - y + 2...
Examine whether the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 are coplanar.
Examine whether the lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 are coplanar.
A family of planes passes through the line of intersection of x + y + z = 1 and 2x + 3y - z = 4 in s...
A family of planes passes through the line of intersection of x + y + z = 1 and 2x + 3y - z = 4 in s...
Two skew lines pass through (1, 2, 3) and (2, 4, 5) with direction vectors (1, 0, -1) and (0, 1, 1) ...
Two skew lines pass through (1, 2, 3) and (2, 4, 5) with direction vectors (1, 0, -1) and (0, 1, 1) ...
Determine the perpendicular distance from the point (1, 2, -1) to the plane whose equation is given ...
Determine the perpendicular distance from the point (1, 2, -1) to the plane whose equation is given ...
Given the point (1, 0, 0) and its reflection across the plane x + y + z = 3, identify the image poin...
Given the point (1, 0, 0) and its reflection across the plane x + y + z = 3, identify the image poin...
Suppose a plane passes through the three non-collinear points (1, 0, 0), (0, 1, 0), and (0, 0, 1) in...
Suppose a plane passes through the three non-collinear points (1, 0, 0), (0, 1, 0), and (0, 0, 1) in...
A directed line segment joins the point (3, 4, 5) to the point (5, 6, 7), so what are its direction ...
A directed line segment joins the point (3, 4, 5) to the point (5, 6, 7), so what are its direction ...
Locate the foot of the perpendicular drawn from the point (1, 2, 3) onto the line given by x/1 = y/2...
Locate the foot of the perpendicular drawn from the point (1, 2, 3) onto the line given by x/1 = y/2...
About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- coplanarity
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
0
- Theory: If four points A,B,C,D lie in the same plane, they have no 'height' relative to each other in 3D space.
- Volume Property: The volume of a tetrahedron formed by three vectors AB,AC,AD is V=61∣AB⋅(AC×AD)∣.
- Result: If the points are coplanar, the vectors are linearly dependent and the scalar triple product is zero, thus V=0.
This easy difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of coplanarity. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse three dimensional geometry questions on RankGuru.