Vector algebra-adding and subtacting vectors


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The mass of your body is a measure of the amount of matter (atoms) that constitute your body. This number is a quantity that can be pinpointed on the x-axis (or any line of numbers). Such quantities are called scalars

It is important here to bear in mind the difference between weight and mass.

The weight is the pull of gravity acting upon any mass within the gravitational field.  This quantity not only has a size but also a direction. It is directed towards the center of gravity of the earth.

Galaxy M 83 15 million light-years away held together by gravity. Courtesy: Anglo-Australian telescope.

Such quantities possessing both mass and direction are termed vectors.

Many important physical quantities are not just quantities (As eg mass, energy and temperature) but  they also have a direction (as e.g. velocities, forces, momentum, pressure, accelerations).

They are usually represented by the length and direction of an arrow or by the coordinates (x, y, z) of the endpoint of the arrow representing the vector beginning at the origin. They are often denoted by a bold letter (F) with an arrow above it.

Position vector

Vectors are added by the polygonal method which means that in order to obtain the vectorsum of several vectors you let the vector number two start at the endpoint of the first vector and so on. After you have drawn all the vectors like this after each other you are able to construct the vectorsum, or resultant, of all the vectors by drawing one vector from the startpoint of the first vector to the endpoint of the last vector.

File:Vectoraddition.svg

A vector can always be divided into x,y, and z-components

F=Fx i+ Fy j+ Fz k.

where i, j, k are the orthogonal unit vectors for the cartesian coordinatesystem.

This gives us the possibility to add vectors algebraically:

 F + G =  (Fx+Gx, Fy+Gy, Fz+Gz) i.e. add the x-coordinates separately and do likewise with the y and z-coordinates to acquire the coordinates of the sum.

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Om mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics
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