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# Vector Algebra Class 12 Formulas

Vectors are mathematical entities that have both magnitude and direction. Vector algebra class 12 formulas are useful in performing numerous arithmetic operations on the same vector and between two vectors. Owing to the different kinds of symbols used in the Vector Algebra Class 12 Formulas these operations often seem confusing to students. But with proper understanding and memorization of vector algebra class 12 formulas, it will become easy for students to solve various problems based on them. This article aims at covering the important list of Vector Algebra Class 12 Formulas along with relevant examples and applications.

## List of Vector Algebra Class 12 Formulas

Given below is a summarized list of vector algebra class 12 formulas:

- Position vector of a point A(a, b, c) is given as \(\overrightarrow {OP} = \overrightarrow {a} =\widehat ai+\hat bj+\hat ck\), and its magnitude is given by \(|(\overrightarrow {OP})|= |\overrightarrow a| = √(a^2 + b^2 + c^2)\)
- The relationship between the magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector can be seen as: l = a/r , m = b/r , c = n/r
- For a given vector a; the unit vector in the direction of is \(\hat a = \overrightarrow {a}/|(\overrightarrow {a})|\)
- The scalar product of two given vectors having angle θ between them is defined as \(\overrightarrow {a} . \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}|Cosθ\)
- If θ is the angle between two vectors \(\overrightarrow a\) and \(\overrightarrow b\), then their cross product is given as\(\overrightarrow {a} × \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}| Sinθ \hat n\)

## Applications of Vector Algebra Class 12 Formulas

The vector algebra class 12 formulas have their applications in solving various real-world problems. Some of them are explained below:

- In physics and engineering, scalar and vector quantities and their algebraic formulas are encountered quite often. Some of the examples of scalar quantities are time, length, mass, speed, volume, while that of the vector quantities are velocity, weight, etc.

- Vector algebra formulas are useful in calculating the amount of solar power generated from solar panels.
- These formulas are applied in space science to calculate the distance and angles between the panels of the satellites.
- In civil engineering, vector algebra class 12 formulas are helpful in performing calculations for building beams and structures.

## Tips to Memorize Vector Algebra Class 12 Formulas

Students will find the below-mentioned tips helpful in remembering the vector algebra class 12 formulas:

**Logical Understanding:** It is necessary to have a clear understanding of the logic behind the formula before moving on to solving problems based on them. Writing down the formula steps and understanding its derivation is also useful.

**Practicing:** Students should practice all the solved examples and problems in textbooks to learn how to apply vector algebra class 12 formulas in various contexts.

**Study Material:** Students can download formula sheets and set the formula images as wallpapers on their mobiles or tablets to ensure a quick revision.

## Vector Algebra Class 12 Formulas Examples

**Example:** What will be the unit vector in the direction of the vector \(\overrightarrow a = \hat i+3\hat j+\hat k\)

**Solution: **The unit vector towards the direction of a vector a is given by \(\hat a = \overrightarrow {a}/|(\overrightarrow {a})|\)

Magnitude of a is \(|\overrightarrow {a}| =\sqrt 1^2+3^2+1^2\)

= (11)

\(\hat a=1/\sqrt 11.(\hat i+3\hat j+\hat k) = 1/\sqrt 11\hat i+3/\sqrt 11\hat j+1/\sqrt 11\hat k\)

Students can download the printable **Maths Formulas Class 12** sheet from below.

## FAQs on Vector Algebra Class 12 Formulas

### What are the Important Vector Algebra Class 12 Formulas?

Some of the important Vector Algebra Class 12 Formulas are listed below:

- Position vector of a point A(a, b, c) is given as \(\overrightarrow {OP} = \overrightarrow {a} =\widehat ai+\hat bj+\hat ck\), and its magnitude is given by \(|(\overrightarrow {OP})|= |\overrightarrow a| = √(a^2 + b^2 + c^2)\)
- The relationship between the magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector can be seen as: l = a/r , m = b/r , c = n/r
- For a given vector a; the unit vector in the direction of is \(\hat a = \overrightarrow {a}/|(\overrightarrow {a})|\)
- The scalar product of two given vectors having angle θ between them is defined as \(\overrightarrow {a} . \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}|Cosθ\)
- If θ is the angle between two vectors a and b, then their cross product is given as\(\overrightarrow {a} × \overrightarrow {b} =|\overrightarrow {a}|.|\overrightarrow {b}| Sinθ \hat n\)

### What are the Basic Vector Algebra Class 12 Formulas?

The basic vector Algebra Class 12 Formulas help students to understand the calculations of unit vectors for a given vector, position vector, its magnitude, relationship between magnitude, direction ratio and direction cosines. Students must understand and apply all these formulas to solve various problems based on them.

### What are the Important Concepts Covered under Vector Algebra Class 12 Formulas?

The important concepts covered in Vector Algebra Class 12 Formulas are the fundamentals of the position vector, its magnitude, direction cosines, direction ratios, the scalar product of two vectors and more. Students can refer to the list of all important vector algebra formulas and concepts explained above.

### How Many Formulas are there in Vector Algebra Class 12 Formulas?

There are around five major Vector Algebra Class 12 Formulas given in this article that the students must go through properly. They will get to know the basic concepts of vectors, different operations on vectors, and algebraic and geometric properties.

### How can I Memorize Vector Algebra Class 12 Formulas?

The following tips can be used on a regular basis by students to remember Vector Algebra Class 12 Formulas:

**Write Down the Formulas**: Writing down the formula several times will help in grasping these formulas quickly as the brain tend to process written information better.

**Practice Solved Examples: **Students are advised to practice all the solved examples first before moving on to the exercise problems as this will get them introduced to the use of formulas in various contexts.

**Take Help of Technology:** Students can set the formula images as wallpapers on their mobiles and laptops to ensure a quick revision.

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