- #1

- 392

- 13

## Homework Statement

Vector u, v, and x are not zero. Vector u + v will be perpendicular (orthogonal) to u-x if

A. |u+v| = |u-v|

B. |v| = |x|

C. u ⋅ u = v ⋅ v, v = -x

D. u ⋅ u = v ⋅ v, v = x

E. u ⋅ u = v ⋅ v

## Homework Equations

u⋅v = |u||v| cos θ

## The Attempt at a Solution

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Two vectors are orthogonal to each other if the dot product is zero.

(u + v) ⋅ (u - x) = 0

(u ⋅ u) - (u ⋅ x) + (v ⋅ u) - (v ⋅ x) = 0

u ⋅ (u + v) - x ⋅ (u + v) = 0

u ⋅ (u + v) = x ⋅ (u + v)

u = x

or

u ⋅ (u - x) + v ⋅ ( u - x) = 0

u ⋅ (u - x) = - v (u - x)

so, u = -v

x = -v

v = -x

It seems the answer is C

But, how to get the condition u⋅u = v⋅v

Thanks in advance