{Vectors}
The component vector of A(-6,2) along B(1,3) is 0.
See (http://www.wolframalpha.com/input/?i=plot+vector+%7B-6%2C+2%7D+%7B1%2C+3%7D)

Why is this the case?
Aren't components of vectors the length of their projections?
Does this mean that the length of this projection would=0?

Help with understanding this would be appreciated.

Question

{Vectors}
The component vector of A(-6,2) along B(1,3) is 0.
See (http://www.wolframalpha.com/input/?i=plot+vector+%7B-6%2C+2%7D+%7B1%2C+3%7D)

Why is this the case?
Aren't components of vectors the length of their projections?
Does this mean that the length of this projection would=0?

Help with understanding this would be appreciated.

anonymous · Answer

(it is 0 because):
(A.B)/|B|=0
(just as an addition)

anonymous · Answer

This question could also be paraphrased as why is the component of A in the direction of B equal to 0 if theta=pi/2

hartnn · Answer

first,those vectors are perpendicular, do u realize that ?

anonymous · Answer

yes

hartnn · Answer

mathematically its easy to show thst there will be no projection....cos pi/2 = 0

anonymous · Answer

yes, what i don't understand is the geometric part i think

hartnn · Answer

|dw:1353171364268:dw|

hartnn · Answer

what will happen to projection if theta will increase and when theta will decrease ?

anonymous · Answer

ahh i think I'm beginning to understand at least intuitively. So the component is something like the shadow (if the sun was shining from straight above)?

anonymous · Answer

if theta increases the length of the component will decrease

hartnn · Answer

yes, like the shadow...

hartnn · Answer

thats correct...

hartnn · Answer

what will happen when theta = pi/2 ?

anonymous · Answer

there will be no shadow ;)

anonymous · Answer

sorry if the primitive analogy isn't to your taste.

hartnn · Answer

u got it :)

anonymous · Answer

but yeah thanks, that helped me understand this.

hartnn · Answer

ok, welcome ^_^