Important Three Dimensional Geometry Formulas For JEE Maths
Three Dimensional Geometry Formulas for JEE play a very big role in exam preparation. JEE Maths important formulas help students solve tough questions quickly. Many problems in JEE 3D Geometry equations need direct formula use. This is why every aspirant should keep a JEE Mains Maths formula sheet ready. The 3D Geometry chapter JEE includes concepts like position vector, distance formula, section formula, direction cosines, equation of a plane, and more.
In both JEE Mains and JEE Advanced 2026, questions from this chapter carry good weight. Learning all important 3D Geometry formulas for JEE Advanced will make problem-solving easier. These formulas are also found in NCERT books and revision sheets like JEE Maths formula sheet provided by different institutes.
Three Dimensional Geometry Formulas for JEE Exam 2026
The 3D Geometry chapter JEE explains points, lines, and planes in space. In 2D, we work with x and y coordinates. In 3D, we add the z-axis to describe objects in space. To prepare well, students must focus on 3D Geometry formulas for JEE Mains as well as important 3D Geometry formulas for JEE Advanced.
Some three dimensional Geometry formulas for JEE, like the equation of a plane formula or the distance formula in 3D geometry, are direct and scoring. Others, like direction cosines and direction ratios formulas, need concept clarity. Keeping all these in one JEE Mains Maths formula sheet makes revision simple.
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Important 3D Geometry Formulas for JEE Advanced 2026
Here is a complete list of formulas that every student should keep in their JEE Maths formula sheet. These are the most important JEE Maths formulas from the 3D Geometry chapter.
Definition: It represents the position of a point in 3D space with respect to the origin.
Formula:
OP = xi + yj + zk
Where:
x = x-coordinate of point P
y = y-coordinate of point P
z = z-coordinate of point P
2. Distance Formula in 3D Geometry
Definition: It calculates the straight-line distance between two points in three-dimensional space.
Formula:
PQ = √((x2 − x1)² + (y2 − y1)² + (z2 − z1)²)
Where:
(x1, y1, z1) = coordinates of point P
(x2, y2, z2) = coordinates of point Q
This is one of the most important 3D Geometry formulas for JEE Mains and is directly asked.
3. Section Formula
Definition: Section formula finds the coordinates of a point dividing a line segment in a given ratio.
Formula:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
z = (mz2 + nz1) / (m + n)
Where:
(x1, y1, z1) = coordinates of point P
(x2, y2, z2) = coordinates of point Q
m, n = ratio parts
This is frequently part of JEE 3D Geometry equations.
4. Direction Cosines and Direction Ratios Formulas
Definition: Direction cosines are cosines of angles that a line makes with the coordinate axes.
Formula:
l = cos α, m = cos β, n = cos γ
Relation:
l² + m² + n² = 1
Where:
α = angle with x-axis
β = angle with y-axis
γ = angle with z-axis
l, m, n = direction cosines
This is one of the JEE Maths important formulas for line-based questions.
5. Equation of a Plane Formula JEE
Definition: Equation of a plane gives the set of all points lying on a flat surface in 3D space.
Formula:
a(x − x1) + b(y − y1) + c(z − z1) = 0
Where:
(x1, y1, z1) = point on the plane
a, b, c = normal vector components
This equation of a plane formula JEE is one of the most used results in exam papers.
6. Equation of a Line in 3D
Definition: It represents a line passing through a point with given direction ratios.
Formula:
(x − x1)/l = (y − y1)/m = (z − z1)/n
Where:
(x1, y1, z1) = given point
(l, m, n) = direction ratios of line
This appears in both 3D Geometry formulas for JEE Mains and JEE Advanced.
7. Centroid of a Triangle
Definition: Centroid is the point where medians of a triangle meet. In 3D, it is the average of vertex coordinates.
Formula:
Centroid = ((x1 + x2 + x3)/3 , (y1 + y2 + y3)/3 , (z1 + z2 + z3)/3)
Where:
(x1, y1, z1), (x2, y2, z2), (x3, y3, z3) = triangle vertices
This is a direct part of JEE Maths formula sheet.
8. Volume of a Tetrahedron
Definition: Volume of a Tetrahedron formula calculates the volume of a tetrahedron formed by four points.
Formula:
V = (1/6) | AB · (AC × AD) |
Where:
AB, AC, AD = vectors from vertex A to other points
This is one of the important 3D Geometry formulas for JEE Advanced.
9. Angle Between Two Lines
Definition: Angle Between Two Lines gives the angle between two lines using their direction cosines.
Formula:
cos θ = l1l2 + m1m2 + n1n2
Where:
(l1, m1, n1) = direction cosines of line 1
(l2, m2, n2) = direction cosines of line 2
θ = angle between the two lines
This is a standard JEE 3D Geometry equation.
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Why 3D Geometry Formulas are Important for JEE
The 3D Geometry chapter JEE is very important because it usually has 2–3 questions in JEE Mains and more weightage in JEE Advanced. Most of these are direct and formula-based, so learning the JEE Maths important formulas helps you save time and score quickly.
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Direct Application in JEE Mains: Many problems are solved directly using 3D Geometry formulas for JEE Mains without long steps.
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Saves Time in Exam: Remembering formulas works like a shortcut and reduces long calculations.
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Covers All Core Topics: The JEE 3D Geometry equations include distance, plane, line, and angle formulas, which cover almost all question types.
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Builds Confidence: A strong grip on the JEE Maths formula sheet makes solving problems quicker and stress-free.
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Crucial for JEE Advanced: The Important 3D Geometry Formulas for JEE Advanced are often tested in tricky and conceptual questions.
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Three Dimensional Geometry Formulas for JEE FAQs
Q1. What are the most important 3D Geometry formulas for JEE Mains?
Ans: The most important 3D Geometry formulas for JEE Mains are the distance formula, section formula, direction cosines, and the equation of a plane formula JEE.
Q2. How many 3D Geometry formulas for JEE Advanced should I memorize?
Ans: You should memorize all important 3D Geometry formulas for JEE Advanced, like the equation of a line, the volume of a tetrahedron, and the angle between lines.
Q3. Where can I find a JEE Mains Maths formula sheet?
Ans: Students can find a JEE Mains Maths formula sheet in NCERT books, coaching materials, and online study guides.
Q4. What is the equation of a plane formula JEE?
Ans: The equation of a plane formula JEE is a(x − x1) + b(y − y1) + c(z − z1) = 0.
Q5. How is the distance formula in 3D geometry used in JEE exams?
Ans: The distance formula in 3D geometry is used to find the distance between two points, or between a point and a line or a plane.
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