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January 27, 2015

January 27, 2015

Posted by **Anonymous** on Sunday, February 10, 2008 at 2:11pm.

a) |u + v| = |u - v|

vector "u" is perpendicular to vector "v"

b) |u + v| > |u - v|

0° ≤ θ ≤ 90°

c) |u + v| < |u - v|

90° < θ ≤ 180°

------- Can you please explain to me why these conditions are true? Why is it perpendicular for the first one? Why is less less than 90°, but greater than 0° for question "b"? Why is it less than 180°, but greater than 90° for question "c"?

- Math: Vectors -
**Damon**, Sunday, February 10, 2008 at 3:20pmLook at resultants

I will call them L and R for left and right

a)

Slope of U = Uy/Ux

Slope of V = Vy/Vx = -1/slope of U if perpendicular = -Ux/Uy

so

Vy/Vx = - Ux/Uy

- Vx Ux = VyUy

Now U + V = (Ux+Vx)i + (Uy+Vy)j

and U - V = (Ux-Vx)i + (Uy-Vy)j

magnitude of U+V squared =

(Ux+Vx)^2 + (Uy+Vy)^2

= Ux^2 + 2 UxVx +Vx^2 +Uy^2+2 UyVy^2+Vy^2

magnitude of U-V squared =

(Ux-Vx)^2 + (Uy-Vy)^2

= Ux^2 [[[[[-2 UxVx ]]]] +Vx^2 etc.

SEE WHAT IS HAPPENING?

If UxVx= - UyVy

those middle terms disappear and the magnitudes squared are the same.

which means that + or - the square roots are the same which means the absolute values are the same

- Math: Vectors -
**Anonymous**, Sunday, February 10, 2008 at 5:10pmNo I don't understand what you did.

- Math: Vectors -

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