Math 12
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7.1 Introduction
7.1 Introduction
7.1.1 Geometric Interpretation of vector
7.1.2 Multiplication of Vector by a Scalar
7.1.3 Addition and Subtraction of Two Vectors
7.1.4 Position Vector
7.1.5 Vectors in a Plane
7.1.6 Properties of Magnitude of a Vector
7.1.7 Another notation for representing vectors in plane
7.1.8 A unit vector in the direction of another given vector
7.1.9 The Ratio Formula
7.1.10 Vector Geometry
Exercise 7.1
7.2 Introduction of vector in Space
7.2 Introduction of vector in Space
7.2.1 Concept of a vector in space
7.2.2 Properties of Vectors
7.2.3 Another notation for representing vectors in space
7.2.4 Distance Between two Points in Space
7.2.5 Direction Angles and Direction Cosines of a Vector
Exercise 7.2
7.3 The Scalar Product of two Vectors
7.3 The Scalar Product of two Vectors
7.3.1 Deductions of the Important Results
7.3.2 Perpendicular (Orthogonal) Vectors
7.3.3 Properties of Dot Product
7.3.4 Analytical Expression of Dot Product u.v (Dot product of vectors in their components form)
7.3.5 Angle between two vectors
7.3.6 Projection of one Vector upon another Vector:
Exercise 7.3
7.4 The Cross Product or Vector Product of Two vectors
7.4 The Cross Product or Vector Product of Two vectors
7.4.1 Derivation of useful results of cross products
7.4.2 Properties of Cross product
7.4.3 Analytical Expression of u x v (Determinant formula for u x v)
7.4.4 Parallel Vectors
7.4.5 Area of Parallelogram
7.4.6 Area of Triangle
Exercise 7.4
7.5 Scalar Triple Product of Vectors
7.5 Scalar Triple Product of Vectors
7.5.1 Analytical Expression of u.(v x w)
7.5.2 The Volume of the Parallelepiped
7.5.3 The Volume of the Tetrahedron
7.5.4 Application of Vectors in Physics and Engineering
Exercise 7.5
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