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<h2 class="title">Properties of Vectors</h2>
<p>Vectors are mathematical objects and we will now study some of their mathematical properties.</p>
<p>If two vectors have the same magnitude (size) <em>and</em> the same direction, then we call them equal to each other. For example, if we have two forces, \(\vec{F_{1}} = \text{20}\text{ N}\) <em>in the upward direction</em> and \(\vec{F_{2}} = \text{20}\text{ N}\) <em>in the upward direction</em>, then we can say that \(\vec{F_{1}} = \vec{F_{2}}\).</p>
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<h3>Definition: Equality of Vectors</h3>
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<p>Two vectors are equal if they have the <strong>same</strong> magnitude and the <strong>same</strong> direction.</p>
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<p>Just like scalars which can have positive or negative values, vectors can also be positive or negative. A negative vector is a vector which points in the direction <em>opposite</em> to the <strong>reference positive direction</strong>. For example, if in a particular situation, we define the upward direction as the reference positive direction, then a force \(\vec{F_{1}} = \text{30}\text{ N}\) <em>downwards</em> would be a <em>negative vector</em> and could also be written as \(\vec{F_{1}} = -\text{30}\text{ N}\). In this case, the negative sign (\(-\)) indicates that the direction of \(\vec{F_{1}}\) is opposite to that of the reference positive direction.</p>
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<h3>Definition: Negative Vector</h3>
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<p>A negative vector is a vector that has the <em>opposite</em> direction to the reference positive direction.</p>
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<p>Like scalars, vectors can also be added and subtracted. We will investigate how to do this next.</p>
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Properties of Vectors

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

Physics

Discover the principles and operations of scalars and vectors such as graphical and algebraic techniques of vector addition, finding magnitude with Pythagoras theorem, and resultant force on a submarine.


Properties of Vectors

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