Difference between revisions of "Points and Vectors"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} | ||
| − | Points and vectors may be entered via [[Input Bar]] in Cartesian or polar coordinates (see [[Numbers and Angles]]). Points can also be created using [[File:Mode point.svg|link=|24px]] [[Point tools]] | + | Points and vectors may be entered via [[Input Bar]] in Cartesian or polar coordinates (see [[Numbers and Angles]]). Points can also be created using [[File:Mode point.svg|link=|24px]] [[Point tools]] and vectors can be created using the [[File:Mode vectorfrompoint.svg|link=|24px]] [[Vector from Point Tool]] or the |
[[File:Mode vector.svg|link=|24px]] [[Vector Tool]] and a variety of [[Commands|commands]]. | [[File:Mode vector.svg|link=|24px]] [[Vector Tool]] and a variety of [[Commands|commands]]. | ||
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{{example|1=<br/> | {{example|1=<br/> | ||
| − | * To enter a point P or a vector ''v'' in Cartesian coordinates you may use <code><nowiki>P = (1, 0)</nowiki></code> or <code><nowiki>v = (0, 5)</nowiki></code>. | + | * To enter a point ''P'' or a vector ''v'' in Cartesian coordinates you may use <code><nowiki>P = (1, 0)</nowiki></code> or <code><nowiki>v = (0, 5)</nowiki></code>. |
| − | * To enter a point in the [[File:Menu view spreadsheet.svg|link=|16px]] [[Spreadsheet View]], name it using its cell address: <code><nowiki>A2 = (1, 0)</nowiki></code> | + | * To enter a point in the [[File:Menu view spreadsheet.svg|link=|16px]] [[Spreadsheet View]], name it using its cell address, e.g.: <code><nowiki>A2 = (1, 0)</nowiki></code> |
* To enter a point in polar coordinates type in <code><nowiki>P = (1; 0°)</nowiki></code> or <code><nowiki>v = (5; 90°)</nowiki></code>. | * To enter a point in polar coordinates type in <code><nowiki>P = (1; 0°)</nowiki></code> or <code><nowiki>v = (5; 90°)</nowiki></code>. | ||
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{{note|You need to use a semicolon to separate polar coordinates. If you don’t type the degree symbol, GeoGebra will treat the angle as if entered in radians.}} | {{note|You need to use a semicolon to separate polar coordinates. If you don’t type the degree symbol, GeoGebra will treat the angle as if entered in radians.}} | ||
| − | Coordinates of points and vectors can be accessed using [[Predefined Functions and Operators|predefined functions]] ''x'' and ''y''. | + | <br> |
| + | Coordinates of points and vectors can be accessed using [[Predefined Functions and Operators|predefined functions]] ''x()'' and ''y()''. | ||
{{Example|1=If <code>P=(1,2)</code> is a point and <code>v=(3,4)</code> is a vector, <code>x(P)</code> returns 1 and <code>y(v)</code> returns 4.}} | {{Example|1=If <code>P=(1,2)</code> is a point and <code>v=(3,4)</code> is a vector, <code>x(P)</code> returns 1 and <code>y(v)</code> returns 4.}} | ||
| − | Polar coordinates of point ''Q'' can be obtained using <code>abs(Q)</code> and <code>arg(Q)</code>. | + | {{note|1=Polar coordinates of point ''Q'' can be obtained using <code>abs(Q)</code> and <code>arg(Q)</code>.}} |
==Calculations== | ==Calculations== | ||
In GeoGebra, you can also do calculations with points and vectors. | In GeoGebra, you can also do calculations with points and vectors. | ||
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}} | }} | ||
==Vector Product== | ==Vector Product== | ||
| − | + | Let ''(a, b)'' and ''(c, d)'' be two points or vectors. Then <code><nowiki>(a, b) ⊗ (c, d)</nowiki></code> returns the z-coordinate of vector product ''(a, b, 0) ⊗ (c, d, 0)'' as single number. | |
Similar syntax is valid for lists, but the result in such case is a list. | Similar syntax is valid for lists, but the result in such case is a list. | ||
Revision as of 14:32, 23 October 2015
Points and vectors may be entered via Input Bar in Cartesian or polar coordinates (see Numbers and Angles). Points can also be created using 
Point tools and vectors can be created using the 
Vector from Point Tool or the
Vector Tool and a variety of commands.
Note: Upper case labels denote points, whereas lower case labels refer to vectors. This convention is not mandatory.
Example:
- To enter a point P or a vector v in Cartesian coordinates you may use
P = (1, 0)orv = (0, 5). - To enter a point in the
Spreadsheet View, name it using its cell address, e.g.: A2 = (1, 0) - To enter a point in polar coordinates type in
P = (1; 0°)orv = (5; 90°).
Note: You need to use a semicolon to separate polar coordinates. If you don’t type the degree symbol, GeoGebra will treat the angle as if entered in radians.
Coordinates of points and vectors can be accessed using predefined functions x() and y().
Example: If
P=(1,2) is a point and v=(3,4) is a vector, x(P) returns 1 and y(v) returns 4. Note: Polar coordinates of point Q can be obtained using
abs(Q) and arg(Q).Calculations
In GeoGebra, you can also do calculations with points and vectors.
Example:
- You can create the midpoint M of two points A and B by entering
M = (A + B) / 2into the Input Bar. - You may calculate the length of a vector v using
length = sqrt(v * v)orlength = Length[v] - If A = (a, b), then
A + 1returns (a + 1, b + 1). If A is a complex number a+bί, thenA+1returns a + 1 + bί.
Vector Product
Let (a, b) and (c, d) be two points or vectors. Then (a, b) ⊗ (c, d) returns the z-coordinate of vector product (a, b, 0) ⊗ (c, d, 0) as single number.
Similar syntax is valid for lists, but the result in such case is a list.
Example:
{1, 2} ⊗ {4, 5}returns {0, 0, -3}{1, 2, 3} ⊗ {4, 5, 6}returns {3, 6, -3}.
