I am a little stuck on how vector decomposition works. Say you draw a vecor A in a 3 dimentional plane. I see that to determin the Ax component, the professor draws an imginary line vertically down from the tip of the A vector down to a point. My question is how does the professor know how far down to draw the imaginary line? It seems to me that the further down you draw the imaginary line the larger the Ax component so you really have not defined a singular and quatifiable Ax component.

Question

I am a little stuck on how vector decomposition works.  Say you draw a vecor A in a 3 dimentional plane.  I see that to determin the Ax component, the professor draws an imginary line vertically down from the tip of the A vector down to a point.  My question is how does the professor know how far down to draw the imaginary line?  It seems to me that the further down you draw the imaginary line the larger the Ax component so you really have not defined a singular and quatifiable Ax component.

anonymous · Answer

First off, there is no such object as a three dimensional plane.  Planes are two dimensional.  But one way to decompose a vector which exists in in three dimensional space is to draw a vertical line from the tip of the vector to the xy-plane as you said.  The length of this line will not affect the value of the x or y components because the line is perpendicular to the xy-plane.  The length of the vertical line gives you the size of the z-component of your vector.  It tells you how many units in the z-direction you have to go from the origin.|dw:1339200967156:dw|