Resultant force from perpendicular vectors

Steps:

• Identify the two forces: 3 N horizontal and 4 N vertical.
• Confirm they are perpendicular (90° angle).
• Apply Pythagorean theorem for magnitude: √(3² + 4²) = √(9 + 16) = √25 = 5 N.
• The resultant is the vector sum, directed at tan⁻¹(4/3) from horizontal.

Why C is correct:

• The magnitude of the resultant for two perpendicular forces follows the Pythagorean theorem: R = √(F₁² + F₂²), yielding exactly 5 N.

Why the others are wrong:

• A: 1 N is the difference if forces opposed, not perpendicular.
• B: 3.5 N approximates average, ignoring vector addition.
• D: 7 N is the arithmetic sum, treating forces as scalars.

Final answer: C