Geometry Formulas For Class 12

Find the best practice material that covers all important geometry formulas for class 12. So that students will not miss any formulas while preparing for board exams or competitive exams. The formulas provided here are as per the CBSE syllabus (2022-2023) and NCERT curriculum. The table below gives you a few important geometry formulas for class 12. The formulas listed below are commonly required in class 12 geometry to calculate directions, length and much more.

List of Geometry Formulas for Class 12

A list of the most commonly used geometry formulas for class 12. Math – Geometry Formulas like Polygon Properties, Area Formulas, Surface Area and Volume Formulas, Circle Formula, Perimeter Formulas.

Vectors and Three Dimensional Geometry Formulas for Class 12
Position Vector
\(\begin{array}{l} \overrightarrow{OP}=\vec{r}=\sqrt{x^{2}+y^{2}+z^{2}}\end{array} \)
Direction Ratios
\(\begin{array}{l} l=\frac{a}{r},m=\frac{m}{r},n=\frac{c}{r}\end{array} \)
Vector Addition
\(\begin{array}{l}\vec{PQ}+\vec{QR}=\vec{PR}\end{array} \)
Properties of Vector Addition
\(\begin{array}{l}Commutative \; Property\; \vec{a}+\vec{b}=\vec{b}+\vec{a}\end{array} \)

\(\begin{array}{l}Associative \; Property\; \left (\vec{a}+\vec{b} \right )+\vec{c}=\vec{a}+\left (\vec{b}+\vec{c} \right )\end{array} \)
Vector Joining Two Points
\(\begin{array}{l}\overrightarrow{P_{1}P_{2}}=\overrightarrow{OP_{2}}-\overrightarrow{OP_{1}}\end{array} \)
Skew Lines (Angle between two lines)
\(\begin{array}{l}\cos\theta = \left | \frac{a_{1}a_{2}+b_{1}b_{2}+c_{1}c_{2}}{\sqrt{a_{1}^{2}+a_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+a_{2}^{2}+c_{2}^{2}}} \right |\end{array} \)
Equation of a Line
\(\begin{array}{l}\frac{x-x_{1}}{a}=\frac{y-y_{1}}{b}=\frac{z-z_{1}}{c}\end{array} \)

More Geometry Formulas for Class 12

  • Vector equation of a line: r = a + λ(b – a), l ∈ R
  • Equation of a line in cartesian form: 
    \(\begin{array}{l}\frac{x-x_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{z-z_{1}}{z_{2}-z_{1}}\end{array} \)
  • Distance between parallel lines: r = a1λb and r = a2 + μb is 
    \(\begin{array}{l}\left|\frac{\vec{b} \times\left(\overrightarrow{a_{2}}-\overrightarrow{a_{1}}\right)}{|\vec{b}|}\right|\end{array} \)
  • Vector form of equation of a plane: r . n = d
  • Cartesian equation of the plane in the normal form: lx + my + nz = d
  • Equation of plane in intercept form: x/a + y/b + z/c = 1


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