## Vectors and Three Dimensional Geometry Formulas for Class 12

## Algebra Formulas For Class 12

**In Vector Addition**

## Trigonometry Class 12 Formulas

**Double Angle and Half Angle Formulas**

### Relations And Functions

*Definition/Theorems*

- Empty relation holds a specific relation R in X as:
**R = φ ⊂ X × X**. - A Symmetric relation R in X satisfies a certain relation as:
**(a, b) ∈ R****implies (b, a) ∈ R**. - A Reflexive relation R in X can be given as:
**(a, a) ∈ R; for all ∀ a ∈ X**. - A Transitive relation R in X can be given as:
**(a, b) ∈ R and (b, c) ∈ R, thereby, implying (a, c) ∈ R**. - A Universal relation is the relation R in X can be given by R = X × X.
- Equivalence relation R in X is a relation that shows all the reflexive, symmetric and transitive relations.

*Properties*

### Inverse Trigonometric Functions

Inverse Trigonometric Functions are quite useful in Calculus to define different integrals. You can also check the Trigonometric Formulas here.

*Properties/Theorems*

The domain and range of inverse trigonometric functions are given below:

*Formulas*

### Matrices

*Definition/Theorems*

**Elementary Operations**

### Determinants

*Definition/Theorems*

- The determinant of a matrix A = [a
_{11}]_{1 × 1}can be given as: |a_{11}| = a_{11}. - For any square matrix A, the |A| will satisfy the following properties:
- (i) |A′| = |A|, where A′ = transpose of A.
- (ii) If we interchange any two rows (or columns), then sign of determinant changes.
- (iii) If any two rows or any two columns are identical or proportional, then the value of the determinant is zero.
- (iv) If we multiply each element of a row or a column of a determinant by constant k, then the value of the determinant is multiplied by k.

*Formulas*

### Continuity And Differentiability

*Definition/Properties*

- A function is said to be continuous at a given point if the limit of that function at the point is equal to the value of the function at the same point.

*Formulas*

Given below are the standard derivatives:

### Integrals

*Definition/Properties*

*Formulas – Standard Integrals*

*Formulas – Partial Fractions*

*Formulas – Partial Fractions*

*Formulas – Integration by Substitution*

*Formulas – Integration by Substitution*

*Formulas – Integrals (Special Functions)*

*Formulas – Integrals (Special Functions)*

*Formulas – Integration by Parts*

- The integral of the product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function}

*Formulas – Special Integrals*

*Formulas – Special Integrals*

### Application Of Integrals

### Vector Algebra

*Definition/Properties*

- Vector is a certain quantity that has both the magnitude and the direction. The position vector of a point P (x, y, z) is given by:

*Formulas*

### Three Dimensional Geometry

*Definition/Properties*

- Direction cosines of a line are the cosines of the angle made by a particular line with the positive directions on coordinate axes.
- Skew lines are lines in space which are neither parallel nor intersecting. These lines lie in separate planes.
- If l, m and n are the direction cosines of a line, then l
^{2}+ m^{2}+ n^{2}= 1.

*Formulas*

### Probability

*Definition/Properties*

- The conditional probability of an event E holds the value of the occurrence of the event F as:

## Frequently Asked Questions – FAQs

### What are the basic maths formulas for class 12th?

The basic formulas that are introduced for class 12th students are for the topics:

Algebra

Geometry

Matrices

Calculus

Linear Programming

Probability

### How many formulas are there in Maths?

There are many formulas in Maths for which we cannot keep a record. Because for each and every concept there are formulas to find the solutions for mathematical problems. Also, for each grade the level of formulas are different.

### What is the importance of Maths formulas?

The importance of learning Maths formulas is that it helps us to solve problems easily. We should have to put the values of entities in the given formula and simplify them. For example, to find the average of a given set of values, we have to need to know first the sum of all those values and number of values. Hence, the average will be equal to the ratio of the sum of values and the number of values.

### What is the formula for integrating trigonometry ratio?

∫cos(a) da = Sin a + C

∫sin (a) da = -Cos a + C

∫sec^2a da = tan a + C

### What is the integration for exponential function?

The value of exponential function e^x remains the same with constant even after integration.

∫e^x dx = e^x + C

*Ques: How many formulas are present in the class 12 CBSE Maths?*

Ans: It is almost next to impossible to keep a record of all the formulas given in the Maths book of class 12 CBSE. As for each and every theory and concept, given in the book, there exist one or more formulas to help find the solutions for the given mathematical problems. As well the level of formulas increases with each grade making class 12 Mathematics the most difficult on the school level.

*Ques: Give a list of basic maths formulas used in CBSE class 12th?*

Ans: A list containing the basic maths formulas that have been introduced for the students of class 12th have been listed in this above article. The basic list of topics include:

1. Algebra

2. Matrices

3. Geometry

4. Linear Programming

5. Calculus

6. Probability

*Ques: What is the formula used for the trigonometric ratio integration?*

Ans: ∫sin (x) dx = -Cos x + C

∫cos(x) dx = Sin x + C

∫sec^2x dx = tan x + C, etc.

*Ques: Why are the mathematical formulas important?*

Ans: The mathematical formulas are important because it helps in solving the mathematical problems with utmost ease. Hence it is important to learn these mathematical formulas for solving the problems in a given time span and in an efficient manner. Mathematical formulas are in the generalized form and at the time of solving the mathematical problems, all we need to do is put the value of entities in the formula given and make the whole process easier and swifter.

*Ques: Where can I find the complete class 12 Mathematics formula for the NCERT book?*

Ans: Students can find the compiled list of formulas in this article on the embibe platform for free. Students can also find direct links to Class 12 Mathematics Notes, Solutions, practice papers, mock tests, important questions, and much more. Students can go through this article to find the complete NCERT Solutions for Class 12 Mathematics along with the links of complete NCERT Book Class 12 Mathematics & important study material.

*Ques: Which is the best solution for NCERT Class 12 Mathematics?*

Ans: Students can find 100 percent accurate Solutions for the NCERT Class 12 Mathematics on the Embibe platform. This article contains the complete solution which has been solved by expert mathematics teachers associated with embibe. We, at Embibe, provide solutions for all the questions given in the Class 12 Mathematics textbook after taking the CBSE Board guidelines under strict consideration from the latest NCERT book for Class 12 Mathematics.

*Ques: What is the formula used for the exponential function integration?*

Ans: If an exponential function is integrated, the function will remain unchanged with a constant being added to it.

Hence, ∫e^x dx = e^x + Constant ©

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