Chapter 7 Vector Math 12th Class Punjab Simulations
Math English Medium Book
- +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
- +7.1 Exercise
- +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
- +7.2 Exercise
- +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:
- +7.3 Exercise
- +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
- +7.4 Exercise
- +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
- +7.5 Exercise
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