Thread: Vectors

What can you conclude about a and b given that

(a)

(b)

I just do not like these open ended questions...I am never sure where to begin.

Recall u*u = ||u||^2

||a +b|| ^2 = (a+b)*(a+b) = ||a||^2 + 2a*b +||b||^2

what does this tell you?

One of the vectors is 0?

no a*b = 0

what does this tell you ?

Ohhh, they are perpendicular?

(How does the second problem differ?)

you now know to answer that yourself.

also it woud be a good time to reconsider what Captain Black had to say

I'm not sure how this differs from part (a) in that it just perpendicular vectors.

I wasn't very clear on what captain black said about c=-b.

remember a - b is a + (-b)

think about it --- consider the vectors i + j and i - j

what is the difference between these 2?

One vector is positive and one is negative?

I'm not trying to sound rude but I have no idea what you are trying to say.

Originally Posted by Zocken

One vector is positive and one is negative?

When



and

So now we are asking: What can you conclude when:



and then what does that mean for and

Does it mean b=0?

or a>b?

Does it mean b=0?

or a>b?

first of all vectors cannot be positive or negative. and it makes no sense

to say things like a > b when and b are vectors.

secondly the point i wanted you to see is that
1. for both i + j and i - j |i+j|^2 = |i|^2 +|j|^2
2. i an j are perpindicular
3. If you graph the vectors notice that i , j and i+j form a right triangle

as does i,j, and i - j which is the point Captain Black was making when he asked you to consider a parallelogram

I think we were both trrying to get you to realize on your own with hints

If
a)

(b)

then a and b are perpindicular period.