Math presentation sam+marius 2
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This math presentation covers vectors in 2 and 3 dimensions. It introduces vectors as quantities that have both magnitude and direction, and covers operations such as vector addition, subtraction and scalar multiplication. It also discusses vector components, scalar products, angles between vectors, parallel vectors, unit vectors, and representations of lines as vectors. The document provides examples and questions on these vector topics.
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Vector analysis involves representing quantities that have both magnitude and direction as vectors. Vectors can be added and subtracted by adding or subtracting the x, y, and z components. The dot product calculates the cosine of the angle between two vectors and is used to find things like work and power. The cross product gives a vector perpendicular to two other vectors and is used to find areas and volumes. Vectors can be represented and transformed between Cartesian, cylindrical, and spherical coordinate systems using transformation matrices.
keph103.pdf
1. The chapter discusses motion in a plane and introduces vectors as a way to describe physical quantities that have both magnitude and direction, such as displacement, velocity, and acceleration.
2. It defines scalars as quantities that only have magnitude and vectors as quantities that have both magnitude and direction, following the triangle law of addition.
3. The chapter then covers adding and subtracting vectors graphically by placing them head to tail, as well as multiplying vectors by real numbers, with negative numbers flipping the direction.
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Vectors have both magnitude and direction, unlike scalars which only have magnitude. Common vector quantities include displacement, velocity, force. Vectors can be added using the parallelogram law or triangle law. The dot product of two vectors produces a scalar, while the cross product produces a vector perpendicular to the two input vectors. Vector concepts like resolution, equilibrium of forces, and area/volume calculations utilize dot and cross products.
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This document discusses physical quantities and units in physics. It defines a physical quantity as something that can be measured, like length, weight, or time, and notes that every physical quantity has a magnitude and unit. It discusses unit conversion for areas and volumes using prefixes like milli (10-3). Base units include meters, kilograms, and seconds. Derived units are combinations of base units and must be multiplied or divided, not added or subtracted. Scalar quantities have only magnitude, while vector quantities have both magnitude and direction, and can be represented by arrows. Methods for adding and resolving vectors are also outlined.
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3-1 VECTORS AND THEIR COMPONENTS
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3.06 Convert a vector between magnitude-angle and unit vector notations.
3.07 Add and subtract vectors in magnitude-angle notation
and in unit-vector notation.
3.08 Identify that, for a given vector, rotating the coordinate
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3) Vectors having both direction and magnitude, while scalars have only magnitude. Vectors can be resolved into x and y components using trigonometry.
3) Vector addition and multiplication using graphical and numerical methods including dot products and cross products.
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4. Motion in a Plane 3.pptx.pptx
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Module No. 21
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Lecture 2 kinematics
This document summarizes key concepts in kinematics including:
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- Displacement, velocity and acceleration are all described as vectors since they have both magnitude and direction.
ch-4 vector and scalar of chapter laws of m
Vectors have both magnitude and direction, while scalars only have magnitude. There are two main types of vector operations: scalar (dot) product and vector (cross) product. The scalar product produces a scalar quantity and results in the magnitudes of the vectors multiplied together. The vector product produces another vector that is perpendicular to the plane of the two original vectors. Vector addition and subtraction can be done geometrically using parallelogram law or analytically by adding/subtracting the corresponding components. Multiplying a vector by a scalar scales its magnitude proportionally while preserving its direction.
Physical quantities and vector representation
This document discusses vectors and the rectangular coordinate system. It defines vectors as physical quantities that require both magnitude and direction, while scalars only require magnitude. Vectors can be represented symbolically with bold letters or graphically with arrows. The rectangular coordinate system uses two perpendicular axes, usually labeled x and y, that intersect at the origin point. Vectors in 2D space are defined by their coordinates on the x and y axes, while vectors in 3D space additionally use a z axis and are defined by their coordinates on all three axes.
02mathematics
The document discusses various coordinate reference frames including Cartesian, polar, cylindrical and spherical coordinates for modeling 2D and 3D objects. It also covers important mathematical concepts for computer graphics like vectors, basis vectors, metric tensors, matrices, and their properties. These concepts are fundamental for representing points, lines, planes and transformations between different coordinate systems in computer graphics applications.
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Math presentation sam+marius 2
- 1. Vectors Math Presentation By Marius and Samuel
- 2. Overview Vectors in 2-dimensions Vectors Operation with Vectors Vectors in Component Form Vector Equations Vectors in coordinate Geometry Parallelism Unit Vectors Angles and Scalar Products Vectors in 3-dimensions 3-dimensional coordinates 3-dimensional Vectors Algebraic operations with 3-D Vectors Parallelism Unit Vectors Collinear points and ratio of division – Extension The scalar product of 3-D Vectors Lines in the plane and in space Vector and parametric form of a line in 2-dimensional Geometry The velocity vector of a moving object Constant velocity Problems The closest distance Geometric application of r = a + tb Lines in Space Line classification
- 3. Vectors in 2-dimensions (2D)
- 4. Vectors Quantities which have only magnitude are called scalars. Quantities which have both size (magnitude) and direction are called vectors. Magnitude can be expressed as: Acceleration Force Displacement Momentum
- 5. Simple representation of a Vector
- 6. VectorEqualityandNegativeVectors Twovectors are equaliftheyhavethesamemagnitude AND direction.
- 7. Question
- 10. Question
- 13. VectorsAddition
- 16. Question
- 17. Lenghtor Magnitude of a Vector
- 19. Question
- 20. ScalarProducts
- 21. VectorsAngle
- 22. Question
- 24. Both in IB Formula Booklet!!
- 25. In IB Formula Booklet!!
- 31. In IB Booklet
- 32. In IB Booklet Booklet also shows the formula isolating for
- 33. In IB Booklet
- 39. Geometric Application of r=a+tb
- 40. Solution
- 41. Lines in Space
- 43. LastQuestion!
- 44. Humour time! The vector was walking down cartesian drive when he bumped into a confused Scalar.The vector asked him what was wrong and he replied, "Help I have no direction.“ HAHAHAHAHAHAHAHAHAHAHAHAHAHAHA