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## Three Dimensional Geometry Maths Formulas for Class 12 Chapter 11

Are you looking for Three dimensional Geometry formulas for class 12 Chapter 11? Today, we are going to share Three dimensional Geometry formulas for class 12 Chapter 11 according to student requirement. You are not a single student who is searching Three dimensional Geometry formulas for class 12 chapters 2. According to me, thousands of students are searching Three dimensional Geometry formulas for class 12 Chapter 11 per month. If you have any doubt or issue related to Three dimensional Geometry formulas then you can easily connect with through social media for discussion. Three dimensional Geometry formulas will very helpful to understand the concept and questions of chapter Three dimensional Geometry.

1. The Direction cosines of a line joining two points P (x1 , y1 , z1) and Q (x2 , y2 , z2) are $$\frac{x_2-x_1}{PQ}\:,\:\frac{y_2-y_1}{PQ}\:,\frac{z_2-z_1}{PQ}$$ where
PQ=$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$
2. Equation of a line through a point (x1 , y1 , z1 ) and having direction cosines l, m, n is: $$\frac{x-x_1}{l}=\frac{y-y_1}{m}=\frac{z-z_1}{n}$$
3. The vector equation of a line which passes through two points whose position vectors $$\vec{a}$$ and $$\vec{b}$$ is $$\vec{r}=\vec{a}+\lambda (\vec{b}-\vec{a})$$
4. The shortest distance between $$\vec{r}=\vec{a_1}+\lambda\: \vec{b_1}$$ and $$\vec{r}=\vec{a_2}+\mu \: \vec{b_2}$$ is:
$$\left | \frac{(\vec{b_1}\times \vec{b_2}).(\vec{a_2}-\vec{a_1})}{|\vec{b_1}\times \vec{b_2}|} \right |$$
5. The distance between parallel lines $$\vec{r}=\vec{a_1}+\lambda\: \vec{b}$$ and $$\vec{r}=\vec{a_2}+\mu \: \vec{b}$$ is
$$\left | \frac{\vec{b}\times (\vec{a_2}-\vec{a_1})}{|\vec{b}|} \right |$$
6. The equation of a plane through a point whose position vector is $$\vec{a}$$ and perpendicular to the vector $$\vec{N}$$ is $$(\vec{r}-\vec{a})\:.\:\vec{N}=0$$
7. Equation of a plane perpendicular to a given line with direction ratios A, B, C and passing through a given point (x1 , y1 , z1) is A (x – x1) + B (y – y1) + C (z – z1) = 0
8. The equation of a plane passing through three non-collinear points (x1 , y1 , z1); (x2 , y2 , z2) and (x3 , y3 , z3) is:
$$\begin{vmatrix} x-x_1& y-y_1& z-z_1\\ x_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1 \end{vmatrix}=0$$
9. The two lines $$\vec{r}=\vec{a_1}+\lambda\: \vec{b_1}$$ and $$\vec{r}=\vec{a_2}+\mu \: \vec{b_2}$$ are coplanar if:
$$(\vec{a_2}-\vec{a_1})\:.\:(\vec{b_1}\times \vec{b_2})=0$$
10. The angle φ between the line $$\vec{r}=\vec{a}+\lambda\: \vec{b}$$ and the plane $$\vec{r}\:.\:\hat{n}=d$$ is given by:
$$sin\:\phi =\left |\frac{\vec{b}\:.\:\hat{n}}{|\vec{b}||\hat{n}|} \right |$$
11. The angle θ between the planes A1x + B1y + C1z + D1 = 0 and A2x + B2y + C2z + D2 = 0 is given by:
$$cos\:\theta =\left | \frac{A_1\:A_2+B_1\:B_2+C_1\:C_2}{\sqrt{A_1^2+B_1^2+C_1^2}\:\sqrt{A_2^2+B_2^2+C_2^2}} \right |$$
12. The distance of a point whose position vector is $$\vec{a}$$ from the plane $$\vec{r}\:.\:\hat{n}=d$$ is given by: $$\left | d-\vec{a}\:.\:\hat{n} \right |$$
13. The distance from a point (x1 , y1 , z1) to the plane Ax + By + Cz + D = 0:
$$\left | \frac{Ax_1+By_1+Cz_1+D}{\sqrt{A^2+B^2+C^2}} \right |$$

#### Summary of Three dimensional Geometry formulas

We have listed top important formulas for Three dimensional Geometry for class 12 Chapter 11 which helps support to solve questions related to chapter Three dimensional Geometry. I would like to say that after remembering the Three dimensional Geometry formulas you can start the questions and answers solution of the Three dimensional Geometry chapter. If you faced any problem to find the solution of Three dimensional Geometry questions, please let me know through commenting or mail.

### Maths Formulas for Class 12 by Chapters

Here Check Maths formulas for class 12 by chapter wise.