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Three Dimensional Geometry formula sheet

Every formula in the Three Dimensional Geometry chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 22 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Coordinates, distance and section formula

Distance and coordinate planes
7× asked, last 2026
PQ=(x2−x1)2+(y2−y1)2+(z2−z1)2distance from the x-axis=y2+z2\begin{aligned}&PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\\&\text{distance from the }x\text{-axis}=\sqrt{y^2+z^2}\end{aligned}
xyxy-plane: z=0z=0; yzyz-plane: x=0x=0; zxzx-plane: y=0y=0. A line meets the yzyz-plane where x=0x=0.
Section formula and centroid
5× asked, last 2026
P=mB±nAm±n,G=A+B+C3P=\frac{mB\pm nA}{m\pm n},\qquad G=\frac{A+B+C}3
++ internal, −- external. The xyxy-plane cuts ABAB in ratio −z1:z2-z_1:z_2. Vertex RR, midpoint MM of the opposite side: G=(2M+R)/3G=(2M+R)/3.

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Practise Three Dimensional Geometry

20 more formulas in 5 topics

Direction cosines and direction ratios; Angle between lines; Equation of a line; Foot, image and distance from a line; and Skew lines and shortest distance. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Direction cosines and direction ratios

  • Direction cosines4×
  • Direction ratios3×
  • Projection of a segment3×
  • DCs from two equations4×

Angle between lines

  • Angle between two lines8×
  • Perpendicular to two lines11×

Equation of a line

  • Point and direction20×
  • Through two points7×
  • Point at distance d9×
  • Intersection of two lines18×
  • Line meeting two lines9×

Foot, image and distance from a line

  • Foot of the perpendicular19×
  • Image in a line22×
  • Distance from a line15×
  • Distance along a direction8×
  • Triangle areas15×

Skew lines and shortest distance

  • Parallel, intersecting or skew3×
  • Shortest distance (skew)41×
  • Distance between parallel lines2×
  • Line of shortest distance4×

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About 295 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Three Dimensional Geometry

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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