Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Vector
A unit vector is a vector that has a magnitude of one and indicates direction. To find a unit vector in the same direction as a given vector, you divide the vector by its magnitude. This process normalizes the vector, preserving its direction while scaling its length to one.
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Magnitude of a Vector
The magnitude of a vector is a measure of its length in space, calculated using the formula √(x² + y²) for a two-dimensional vector. For the vector v = 8i - 6j, the magnitude is √(8² + (-6)²) = √(64 + 36) = √100 = 10. This value is essential for normalizing the vector to find the unit vector.
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Vector Components
Vectors in two dimensions can be expressed in terms of their components along the x-axis and y-axis, typically denoted as ai + bj. In the vector v = 8i - 6j, '8' is the x-component and '-6' is the y-component. Understanding these components is crucial for calculating the magnitude and subsequently finding the unit vector.
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