Mathematicians and scientists call a quantity which depends on direction a vector quantity, and a quantity which does not depend on direction is called a scalar quantity. Vector quantities have two characteristics, a magnitude and a direction. Scalar quantities have only a magnitude. When comparing two vector quantities of the same type, you have to compare both the magnitude and the direction. For scalars, you only have to compare the magnitude. When doing any mathematical operation on a vector quantity (like adding, subtracting, multiplying...) you have to consider both the magnitude and the direction. This makes dealing with vector quantities a little more complicated than scalars. On the slide we list some of the physical quantities discussed in the Beginner's Guide to Propulsion and group them into either vector or scalar quantities. Of particular interest, the forces, which operate on a flying aircraft, the weight, thrust, and aerodynamic forces, are all vector quantities. The resulting motion of the aircraft in terms of displacement, velocity, and acceleration are also vector quantities. These quantities can be determined by application of Newton's laws for vectors. The scalar quantities include most of the thermodynamic state variables involved with the propulsion system, such as the density, pressure, and temperature of the propellants. The energy, work, and entropy associated with the engines are also scalar quantities. There are some quantities, like speed, which have very special definitions for scientists. By definition, speed is the scalar magnitude of a velocity vector. A car going down the road has a speed of 50 mph. Its velocity is 50 mph in the northeast direction. It can get very confusing when the terms are used interchangeably! While Newton's laws describe the resulting motion of a solid, there are special equations which describe the motion of fluids, gases and liquids, through the propulsion system. For any physical system, the mass,...

...SCALAR Quantities
Scalar is the measurement of a medium strictly in magnitude. It is a physical quantity that is unchanged by coordinate system rotations or reflections (in Newtonian mechanics), or by Lorentz transformations or space-time translations (in relativity).
A scalar is a quantity which can be described by a single number, unlike vectors, tensors, etc. which are described by several numbers which describe magnitude and...

...
Acceleration
Velocity
Displacement
Distance
Time
Definition
1. Acceleration is the rate of change of velocity with time.
Velocity is a vector physical quantity; both magnitude and direction are required to define it.
the length of an imaginary straight path, typically distinct from the path actually travelled by P.
Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, or an estimation...

...HL Vectors Notes
1.
Vector or Scalar
Many physical quantities such as area, length, mass and temperature are completely described once the magnitude of the quantity is given. Such quantities are called “scalars.” Other quantities possess the properties of magnitude and direction. A quantity of this kind is called a “vector” quantity. Winds are usually described by giving their speed and direction; say 20 km/h...

...Calculus in 3D Geometry, Vectors, and Multivariate Calculus Zbigniew H. Nitecki
Tufts University
August 19, 2012
ii
This work is subject to copyright. It may be copied for non-commercial purposes.
Preface
The present volume is a sequel to my earlier book, Calculus Deconstructed: A Second Course in First-Year Calculus, published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at...

...December 2011
Vectors
Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH...

...
1a. h=-4.9t^2+450
1b. h(t)=-4.9t^2+450
(h(2)-h(0))/(2-0)
((-4.9(〖2)〗^2+450)-(-4.9(0)^2+450))/2
=(430.4-450)/2
=-19.6
∴The average velocity for the first two seconds was 19.6 metres per second.
c. i)
i)
=
=-24.5
∴ The average velocity from is 24.5 metres/s.
ii)
= -14.7
iii)
= -12.25
∴ The average velocity from is 12.25 metres/s.
d) Instantaneous velocity at 1s:
=-9.8
∴ The...

...Mehran University College
Of Engineering & Technology,
Khairpur Mir’s
VECTOR GROUPS
ENGR. AHSANULLAH MEMON
LECTURER
DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS
ZIGZAG CONNECTION OF TRANSFORMER
The zigzag connection of tranformer is also called the
interconnected star connection.
This connection has some of the features of the Y and
the ∆ connections, combining the advantages of both.
The zigzag transformer contains six coils on three
cores.
Its...

...is a vector which represents the initial state of a system, then there is a matrix M such that the state of the system after one iteration is given by the vector M x0 . Thus we get a chain of state vectors: x0 , M x0 , M 2 x0 , . . . where the state of the system after n iterations is given by M n x0 . Such a chain is called a Markov chain and the matrix M is called a transition matrix. The state vectors can be of one of two types: an...

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