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184_notes:math_review [2018/05/17 13:33] – [Vector Notation] curdemma | 184_notes:math_review [2018/05/17 13:36] – [Unit Vectors] curdemma | ||
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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 | + | 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:// |
$$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | $$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | ||
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$$\vec{a} = |\vec{a}|\hat{a}$$ | $$\vec{a} = |\vec{a}|\hat{a}$$ | ||
- | We also use unit vectors to describe the x, y, and z coordinate directions. | + | We also use unit vectors to describe the x, y, and z coordinate directions. |
$$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | $$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | ||
$$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ | $$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ |