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Vectors1

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الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 2
أستاذ المادة هدى عامر هادي       21/03/2021 22:31:17

In this chapter we will take a look at vectors and some of their properties. We will study some of the preliminary principles of vectors and some operations on vectors.
Vectors
Lots of things get measured in amounts, e.g. mass, time, temperature. More things have a magnitude and direction, e.g. displacement, velocity, force. Quantities with both a magnitude and a direction can be represented by vectors. It’s helpful to think of vectors by drawing them as arrows on paper.


Def1. The vector is quantity with magnitude and denoted by v ?,(v ??R^2 or v ??R^3 ).
Def2. The vector represented by the directed line segment (AB) ? has initial point A and terminal point (end point) B and its length is denoted by |(AB) ? |. Two vectors are equal if they have the same length and direction.
(v ??R^2 او v ??R^3 ) (,v) ? .



Properties of vectors:-
The vectors are equal if they have the same length and direction.
Add two vectors is also vector.
Subtract two vectors is also vector.
A vector v ? and a scalar c (c is real number):-
cv ? is the same direction of v ?, if c is positive.
cv ? is opposite direction of v ?, if c is negative.

Def3. If v ? is a two-dimensional vector in the plane equal to the vector with initial point at the origin and terminal point ?v_1,v_2 ?, then the component form of v ? is
v ?=?v_1,v_2 ?
If v ? is a three-dimensional vector in the plane equal to the vector with initial point at the origin and terminal point ?v_1,v_2,v_3 ?, then the component form of v ? is
v ?=?v_1,v_2,v_3 ?

Def4. The vector v ? in two-dimension (Cartesian plane) equal with point at the origin O (0,0) and the end point at (x,y) v ?=(OP) ? .
b P(x,y)


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