# Math: Vectors

posted by .

What conditions must be satisfied by the vectors "u" and "v" for the following to be true?

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 -

Look 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 -

No I don't understand what you did.

## Similar Questions

1. ### physics-vectors

If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then: If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: a. the scaler product of the vectors must …
2. ### Math: Vectors

Find any vector w that is perpendicular to both vector "u = 3j + 4k" and vector "v = 2i". Note: i, j and k are unit vectors How would you solve this problem?
3. ### physics [vectors]

The concept i get, but somehow i just can't execute this problem, please help me! You are given vectors A = 5.5 6.2 and B = - 3.7 7.4 . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product …
4. ### Mamthematics - Vectors

a) If vector u and vector v are non-collinear vectors show that vector u, vector u cross product vector v and (vector u cross product vector v) cross product vector u are mutually othogonal. b) Verify this property using vectors collinear …
5. ### maths

Given that vector c and vector d are non zero vectors such that vector c =x1i + y1j + z1k and vector d =(y1z2-y2z1)+(x1y2 -x2y1)show that the two vectors are perpendicular.
6. ### Calculus

1. Find an ordered pair that represents 6 vector v - 5 vector w if vector v =(9,5) and vector w = (6,9). 2. Find an ordered triple that represents 6 vector y + 4 vector z if vector y = (2,6,8) and vector z = (7,-2,6) 3. Find the magnitude …