Vectors, superposition and interference of waves

[Gear300]

I ran into this problem while working on superposition and interference of waves...its bugging the crap out of me...mind hasn't been working well lately...

A horizontal line intersects a vertical line to form a quadrant with the intersection being the origin. There are 2 vectors, r1 and r2, that extend from the same point on the horizontal line to 2 different points, y1 and y2, on the vertical line (r2 being higher than r1). Breaking each vector into their components, one would notice that both share the same horizontal displacement. Therefore, deltar = r2 - r1 = (y2 - y1)j, j being the vertical unit vector. However, when taking r2 = sqr(x^2 + y2^2) and r1 = sqr(x^2 + y1^2) (sqr being a square root function), r2 - r1 is equal to something different from r2 - r1. Why does this difference exist?

 

[Gear300]

ಠ_ಠ??

 

[LowlyPion]

I ran into this problem while working on superposition and interference of waves...its bugging the crap out of me...mind hasn't been working well lately...

A horizontal line intersects a vertical line to form a quadrant with the intersection being the origin. There are 2 vectors, r1 and r2, that extend from the same point on the horizontal line to 2 different points, y1 and y2, on the vertical line (r2 being higher than r1). Breaking each vector into their components, one would notice that both share the same horizontal displacement. Therefore, deltar = r2 - r1 = (y2 - y1)j, j being the vertical unit vector. However, when taking r2 = sqr(x^2 + y2^2) and r1 = sqr(x^2 + y1^2) (sqr being a square root function), r2 - r1 is equal to something different from r2 - r1. Why does this difference exist?

Because you are comparing the magnitudes of two vectors, that by definition lay along different paths. The Vector subtraction yields the vector of magnitude Y2 - Y1. The difference in the hypotenuses don't apply.

 

[Gear300]

I see...its due to the directional factor...