Explanation:

Let's examine the statements:

- You are given:

  X² + Y² = 1

  u² + v² = 1

  x·u + y·v = 0

- (1) x² + u² = 1

  – This is NOT necessarily true. We only know X² + Y² = 1 and u² + v² = 1, not their individual combinations.

- (2) y² + v² = 1

  – Also NOT necessarily true for the same reason as above.

- (3) xy + uv = 0

  – There's no information to suggest this must be true unless extra context is given (like orthogonality or specific vector conditions).

- None of (1), (2), (3) must be true just from the information provided.

Options:

- 1, 3 only – Incorrect

- 1 and 2 only – Incorrect

- 1, 2 and 3 – Incorrect

- 2 and 3 only – Incorrect

Correct answer: Actually, none of the options are correct since none of the statements can be assuredly concluded.