# Sum of vector

1. Jan 18, 2014

### negation

1. The problem statement, all variables and given/known data

The sum of two vectors, A→ + B→, is perpendicular to their difference, A→ - B→. How do the vectors magnitude compare?

3. The attempt at a solution

SQRT[(A+B)^2 + (A-B)^2]

2. Jan 18, 2014

### voko

Have you studied the scalar (dot) product of vectors?

3. Jan 18, 2014

### negation

I have but only very briefly-1 lecture class on that and that was 1 semester back. But, if you could give me a rough overview, I'll build on those knowledge.

4. Jan 18, 2014

### BvU

What does perpendicularity mean for the dot product ? write it out as a vector expression, then use the distributive property of the dot product.

5. Jan 18, 2014

### negation

It means A→.B→ = 0

6. Jan 18, 2014

### BvU

Right. Now A+B is perpendicular to A-B, so: (A+B).(A-B)=0

7. Jan 18, 2014

### negation

Dot product implies that the product of two vector A→.B→ = 0

Let A→+B→ = R1 $\wedge$ A→-B→= R2

R1.R2 = 0

(A→+B→).(A→-B→) = A^2→ - B^2→ = 0

A=B

8. Jan 18, 2014

### BvU

Bingo.

9. Jan 18, 2014

### voko

See, it was not that hard :)

10. Jan 18, 2014

### negation

It wasn't but my interpretation was different. I went in with the assumption
1) A right angle triangle exists.
2) the length parallel to the y-axis = r1
3) length perpendicular to r1 = r2
4) find the resultant

11. Jan 18, 2014

### voko

I do not understand how your assumption is related to the problem.

12. Jan 18, 2014

### negation

I interpreted the question wrongly and build assumptions on the wrong premise.