Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Next revisionBoth sides next revision | ||
184_notes:math_review [2018/05/17 13:33] – [Vector Notation] curdemma | 184_notes:math_review [2018/05/17 13:38] – [Vector Addition] curdemma | ||
---|---|---|---|
Line 38: | Line 38: | ||
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:// |
$$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | $$a = | \vec{a} | = \sqrt{a_x^2+a_y^2+a_z^2}$$ | ||
Line 50: | Line 50: | ||
$$\vec{a} = |\vec{a}|\hat{a}$$ | $$\vec{a} = |\vec{a}|\hat{a}$$ | ||
- | 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. |
$$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | $$\vec{a} = a_x\hat{x}+a_y\hat{y}+a_z\hat{z}$$ | ||
$$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ | $$\vec{a} = a_x\hat{i}+a_y\hat{j}+a_z\hat{k}$$ | ||
Line 56: | Line 56: | ||
==== Vector Addition ==== | ==== Vector Addition ==== | ||
- | {{ course_planning: | + | [{{ course_planning: |
- | {{ course_planning: | + | [{{ course_planning: |
Two vectors are added (or subtracted) component by component: | Two vectors are added (or subtracted) component by component: | ||
$$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle | $$ \vec{a} +\vec{b} = \langle a_x, a_y, a_z \rangle + \langle b_x, b_y, b_z \rangle = \langle a_x+b_x, a_y+b_y, a_z+b_z \rangle |