- #1
terryds
- 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