CHAPTER 10

VECTOR ALGEBRA

VECTOR ALGEBRA

• All physical quantities have been classified in to two categories- Scalars and Vectors
• Scalar:- Physical quanties having only magnitude are called scalars. eg:-speed,distance,temparature,mass,volume etc
• Vectors:- Physical quantities having both magnitude and direction are called vectors. eg:- Velocity,displacement,acceleration,force,momentum etc

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Representation and Notation

• A vector is represented by a directed line segment.
• The magniute or the modulus of the vector AB is denoted by I AB I or AB
• The magnitude of a vector is a non negative real number.

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Type of Vectors

• Collinear Vectors:- Vectors lying on the same straight line or on parrallel lines are called collinear vectors
• Coplanar Vectors:- Vectors lying on the same plane or on parrallel planes are called coplanar vectors.
• Co-initial vectors:-vectors having the same initial point are called co-initial vectors.
• Co-terminous vectors :-Vectors having the same terminal point are called co-terminus vectors.

Addition of Vectors

Parallelogram law of Vector Addition

• If the two vectors a and b are placed such that the initial points are coinciding then the diagonal of the parrallelogram formed with adjacent sides a and b ,and also passing through the initial points,is the sum of the vectors a and b

Multiplication of a vector by a scalar

Properties of Vector Addition and Scalar Multiplication

Position Vector of Point

External Division

• https://www.geogebra.org/classic/stzznr3x

PRODUCT OF VECTORS

Properties of dot product:-

� Projection of a vector along another vector �

GEOMETRICAL MEANING OF SCALAR PRODUCT�

Questions for Practice

Cross Product (Vector Product)Of Two Vectors

Properties Of Vector Product

Geometrical Meaning of Vector Product

Scalar Tripple Product (Box Product)

• Three nonzero vectors are coplanar iff the box product is zero.

• THE END