Two vectors $u, v$ are ORTHOGONAL iff
A$u = v$
B$\|u\| = \|v\|$
C$u \cdot v = 0$
D$u + v = 0$
Answer & Solution
Correct answer: C. $u \cdot v = 0$
1. ORTHOGONAL: vectors $u, v$ are orthogonal iff their INNER PRODUCT (dot product) is zero: $u \cdot v = 0$.
2. Geometrically: in $\mathbb{R}^n$, this corresponds to the vectors being PERPENDICULAR (at 90°).
3. NOTE: the zero vector is orthogonal to EVERY vector.
4. ORTHONORMAL set: orthogonal AND each $\|u_i\| = 1$.
5. Other options describe other relationships.
_Source: Sergei Treil, "Linear Algebra Done Wrong", §5.1 (Inner products and orthogonality)._
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