[color=#134f5c][size=150][b]The cross product [/b]of any 2 vectors [b]u[/b] and [b]v[/b] is yet [b]ANOTHER VECTOR! [/b][br][br]In the applet below, vectors [b]u [/b]and[b] v[/b] are drawn with the same initial point. [br][br]The [b]CROSS PRODUCT[/b] of u and v is also shown [b](in brown)[/b] and is drawn with the same initial point as the other two. [br][br]Interact with this applet for a few minutes by moving the[b] initial point[/b] and [b]terminal points[/b] of both vectors around. [br][br]Then, answer the questions that follow. [/size][/color]
Use GeoGebra to measure the angle at which the line containing [b]u[/b] intersects the line containing the [b][color=#980000]cross product [/color][/b]vector. What do you get?
Use GeoGebra to measure the angle at which the line containing [b]v[/b] intersects the line containing the [b][color=#980000]cross product [/color][/b]vector. What do you get?
Given your responses for (1) and (2) above, what can we conclude about the [b][color=#980000]cross product[/color][/b] of any two vectors with respect to both individual vectors themselves?
Is it possible to position vectors [b]u[/b] and [b]v[/b] so that their [b][color=#980000]cross product = the zero vector[/color][/b]? If so, how would these 2 vectors be positioned?
How would vectors [b]u [/b]and [b]v[/b] have to be positioned in order for their [b][color=#980000]cross product[/color][/b] to have the greatest magnitude? Use GeoGebra to help informally support your conclusion(s).