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184_notes:math_review [2018/05/17 13:21] – [Math Review] curdemma | 184_notes:math_review [2018/05/17 13:34] – [Vector Notation] curdemma | ||
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==== Vector Notation ==== | ==== Vector Notation ==== | ||
- | {{ course_planning: | + | [{{ course_planning: |
- | Vectors are typically drawn as an arrow. The length of the arrow represents the magnitude of the vector, and the arrow points in the same direction as the vector. The triangle end of the arrow is typically referred to as the " | + | Vectors are typically drawn as arrows. The length of the arrow represents the magnitude of the vector, and the arrow points in the same direction as the vector. The triangle end of the arrow is typically referred to as the " |
We can also define a vector in " | We can also define a vector in " | ||
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where $a_x$, $a_y$, and $a_z$ are the vector components in the $x$, $y$, and $z$ direction respectively. They tell you "how much" of the vector $\vec{a}$ is aligned with each coordinate direction. The vector itself is denoted either in bold face (typical in textbooks) or with an arrow above it. | where $a_x$, $a_y$, and $a_z$ are the vector components in the $x$, $y$, and $z$ direction respectively. They tell you "how much" of the vector $\vec{a}$ is aligned with each coordinate direction. The vector itself is denoted either in bold face (typical in textbooks) or with an arrow above it. | ||
- | The magnitude (or length of a vector) is a scalar quantity and is denoted by vertical lines on either side of the vector. It can be found by using the [[https:// | + | The magnitude (or length of a vector) is a scalar quantity and is denoted by vertical lines on either side of the vector |
$$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | $$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | ||