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What information do you need to fully define a vector?
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Let’s begin by considering the two-dimensional 𝑥𝑦 plane as shown.
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The arrow drawn represents a vector.
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There are two ways that we could define this.
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Firstly, any vector has both magnitude and direction.
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The length of the line segment drawn is the magnitude of the vector, and the arrow indicates the direction.
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The start point for a vector is sometimes known as its tail, and the endpoint is known as the head.
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The direction of any vector is, therefore, from its tail to its head.
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This means that we also have a second way of defining a vector if we know its initial point or tail and terminal point or head.
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We can, therefore, conclude that there are two pieces of information that we need to define a vector, either its magnitude and direction or its initial and terminal points.