Monday

April 21, 2014

April 21, 2014

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 -

**Related Questions**

physics-vectors - If the magnitude of the sum of two vectors is greater than the...

calculus - What conditions must be satisfied by vectors u and v for this to be ...

Calculus - 1. Find an ordered pair that represents 6 vector v - 5 vector w if ...

cartesian vectors 2 - let vector U = (vector u1, vector u2) vector V = (vector ...

Mamthematics - Vectors - a) If vector u and vector v are non-collinear vectors ...

math - If A^TA is an invertible matrix, prove that the column vectors of A are ...

Discrete Math - Geometric Vectors - Under what conditions will 3 vectors having ...

Math - Algebraic Vectors - Given the vectors: u = [3, 0] v = [-1, 2] a) Express ...

12th grade - prove that normal to plane containing 3 points whose position ...

Calculus and vectors - Please help/verify the answer. 1. When you add vectors ...