Difference between revisions of "Cross Command"

Latest revision as of 12:40, 5 October 2017

Cross( <Vector u> , <Vector v> ): Calculates the cross product of u and v. Instead of vectors you can also use lists.; Example:
Cross((1, 3, 2), (0, 3, -2)) yields (-12, 2, 3), Cross({1, 3, 2}, {0, 3, -2}) yields {-12, 2, 3}

For 2D vectors or points the result is the z-coordinate of the actual cross product.

Example: Cross((1,2),(4,5)) yields -3.

Hint: If a vector in the

CAS View contains undefined variables, the command yields a formula for the cross product, e.g. Cross((a, b, c), (d, e, f)) yields (b f - c e, -a f + c d, a e - b d).

Notes:

You can also use the operator u ⊗ v
See also Dot Command.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.0}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|vector-matrix}}
-{{command|CAS}}
+;Cross( <Vector u> , <Vector v> )
-;Cross[ <Vector u> , <Vector v> ]
+:Calculates the [[w:Cross_product|cross product]] of ''u'' and ''v''. Instead of vectors you can also use lists.
-:Calculates the cross product of ''u'' and ''v''.
+:{{example| 1=<div><code><nowiki>Cross((1, 3, 2), (0, 3, -2))</nowiki></code> yields ''(-12, 2, 3)'', <code><nowiki>Cross({1, 3, 2}, {0, 3, -2})</nowiki></code> yields ''{-12, 2, 3}''</div>}}
-:For vectors ''u=(a,b)'' and ''v=(c,d)'' returns ''ad-bc'' (i.e. the z-coordinate of vector product of ''(a,b,0), (c,d,0)'').
+:For 2D vectors or points the result is the z-coordinate of the actual cross product.
-:{{example| 1=<div><code><nowiki>Cross[{1, 3, 2}, {0, 3, -2}]</nowiki></code> gives ''{-12, 2, 3}'', the cross product of ''{1, 2, 3}'' and ''{0, 3, -2}''.</div>}}
+:{{example|<code><nowiki>Cross((1,2),(4,5))</nowiki></code> yields -3.}}
-{{note| 1=<div>
+{{hint|1=If a vector in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]] contains undefined variables, the command yields a formula for the cross product, e.g.
-*In the [[Input Bar]] you can also use <code>u⊗v</code>.
+<code><nowiki>Cross((a, b, c), (d, e, f))</nowiki></code> yields ''(b f - c e, -a f + c d, a e - b d)''.
-*See also [[Dot Command]].
+}}
-</div>}}
+{{notes| 1=
+* You can also use the [[Predefined_Functions_and_Operators|operator]] <code><nowiki>u ⊗ v</nowiki></code><div>
+* See also [[Dot Command]].</div>}}

Difference between revisions of "Cross Command"

Latest revision as of 12:40, 5 October 2017

Cross

Command Categories (All commands)