Plus Two Maths Notes Chapter 10 Vector Algebra is part of Plus Two Maths Notes. Here we have given Plus Two Maths Notes Chapter 10 Vector Algebra.

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus Two |

Subject | Maths Notes |

Chapter | Chapter 10 |

Chapter Name | Vector Algebra |

Category | Plus Two Kerala |

## Kerala Plus Two Maths Notes Chapter 10 Vector Algebra

**Unit vector:**A vector whose magnitude is lo unity.

Unit vector in the direction of

**Vector joining two points.**

Let A(x_{1}, y_{1}, z_{1}) and B (x_{2}, y_{2}, z_{2}) be two points, then = Position vector of B Position vector of A

**Direction Cosines.**

Let the position vector is of a point

P (x, y, z). make angles α, β, r with the positive direction of x, y & z respectively.

α, β, r are direction angles cosα, cosβ, cosr are direction cosines.

t = cosα = m = cosβ = n = cosr =

cos^{2}α + cos^{2}β + cos^{2}r = 1 i.e., l^{2}+ m^{2}+ n^{2}= I

the number which are proportional to the direction cosines of a vector is te direction ratios of the vecto . Denoted by a, b, c. a^{2}+ b^{2}+ c^{2}= l^{2}r^{2}+ m^{2}r^{2 }+ n^{2}r^{2 }**Zero vector.**Vector whose initial & terminal points coincide.**Coinitial vector**. Two or more vectors having the same initial point.**Equal vectors.**Two vectors and are said to be equal, if they have the same magnitude & direction.**Collineanty of two vectors.**- Two vectors and are collinear if and only if there exists a non-zero scalar λ such that
- = and

= are collinear if and only if

**Vector addition.**- Triangular law of vector addition
- Parallelogram law of vector addition

**Properties of vector addition:**- (commulative property)
- (Associative property)
- ( is additive identity)

- Two vectors and are parallel, then

= λ, where λ is a scalar. - Addition and multiplication by a scalar.

Let k and m be any scalars, then

**Collinearity of three points:**Three points A, B, and C are collinear, then

where λ is a scalar.

**Section Formula**

If and be the position vectors of the points A and B respectively, then the position vector of the point which divides AB in the ratio m: n internally is

The position vector of the mid-point of

AB is

**Product of Two Vectors**

**I. Scalar (or dot) product.**

where θ is the angle between and , 0 < θ < π

- Geometrically (Projection of on )
- . Projection of b on a =

- Projection of a on b =

- is a real number.
- = 0 ⇔ , where and are two non-zero vectors.

- The angle between two non-zero vectors and is given by cosθ =

- Scalar product in terms of rectangular components:

**II Vector (or cross) product.**

where θ is the angle between and ,

0 < θ < π, and is the unit vector perpendicular to both and so that

,, form a right handed system. - Geometrical interpretations:

(1) Area of the parallelogram with adjacent sides and =

(ii) Area of the triangle with adjacent

sides and - is a vector
- = ⇔ , where and are two non-zero vectors.

- The angle between two vectors and is given by, sin θ =

- Vector product in terms of rectangular components

- The vector perpendicular to both and =
- Unit vector perpendicular to the plane of and :

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