The unit vector having the opposite direction of the vector (1, −1) is

Question

The unit vector having the opposite direction of the vector (1, −1) is

1. A. (1/√2)(1, −1)
2. B. (-1/√2)(1, −1) (Correct answer)
3. C. (-1, 1)
4. D. (1, −1)

Correct Answer

Option B — (-1/√2)(1, −1)

Detailed Solution & Explanation

The correct answer is (-1/√2)(1, −1).

Key Points

• Vector (1,−1) has magnitude √2. Unit vector in same direction = (1/√2)(1,−1).
• The OPPOSITE direction unit vector = (−1/√2)(1,−1).

Additional Information

• A unit vector is a vector divided by its own magnitude: â = a/|a|, so it has length 1 and keeps the direction.
• For (1, −1) the magnitude is √(1² + 1²) = √2, giving (1/√2)(1, −1).
• The opposite direction is obtained by negating: −â. Magnitude is unchanged; only the sense reverses.
• Unit vectors are how directions are specified independently of length — the standard basis vectors i, j and k are the simplest examples.