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Symbolically, a vector is notated with an arrow on top of it when hand-written. The symbol \\(\\vec{A}\\) would be read as “vector A.” When typed, we use a bold-faced font. So, the symbol A<\/strong> would also be read as “vector A.”<\/p>\n\n\n\n The length of the arrow gives the magnitude<\/em> of the vector. Magnitude is a scalar quantity. The magnitude of a vector A<\/strong> can be written as \\(|\\vec{A}|\\), \\(|\\mathbf{A}|\\), \\(|A|\\), or simply \\(A\\) (just the letter, neither bold-faced nor with an arrow on top). When written as \\(A\\), you need to consider the context to recognize if you are working with the magnitude of a particular vector. In this chapter, I will explicitly note a vector’s magnitude using absolute value bars. In future chapters, I will use the simpler and more common notation without absolute value bars or an arrow.<\/p>\n\n\n\n Now imagine that you build an arrow out of planks of wood. You then hold the arrow up at an angle, and shine a flashlight directly down from above the arrow*<\/a><\/sup>. You would see a shadow cast along the ground, under the arrow.<\/p>\n\n\n\n Then pretend that you could do that with the arrow in figure above. You would see its shadow cast along the x-axis. The length of this arrow would give the \\(x\\) component<\/em> of the vector. The components of a vector tell you how much that vector points in a particular direction. For a vector in lying in a 2-dimensional plane, using \\(x\\) and \\(y\\) Cartesian coordinates, we write out the vector as follows:<\/p>\n\n\n \\[ \\vec{A} = A_x\\hat{x} + A_y\\hat{y} \\tag{2.1} \\]<\/p>\n\n\n\n This is called being written in component form<\/em>, and is a very common way you will see vectors written out. The components \\(A_x\\) and \\(A_y\\) (pronounced “A ex” and “A why” or “A sub ex” and “A sub why”) are scalars. The symbols \\(\\hat{x}\\) and \\(\\hat{y}\\) (pronounced “ex hat” and “why hat”) represent vectors with a magnitude of 1, often referred to as unit vectors<\/em>, which point in the direction of the x-axis and y-axis respectively.**<\/a><\/sup> The vector \\(\\vec{A}\\) basically gives directions saying “go \\(A_x\\) units in the \\(x\\) direction, and \\(A_y\\) units in the \\(y\\) direction.<\/p>\n\n\n\n You may use the interactive below to see many examples of vectors represented as arrows, and with the corresponding vector notation. Use the sliders at the top to adjust the x<\/em> and y<\/em> components of the vector.<\/p>\n\n\n\n\nExample 2.3<\/h4>\n\n\n\n