Resultant of perpendicular forces: 6 N and 8 N at right angles Two forces of 6 N and 8 N act at right angles to each other. What is the magnitude of their resultant?

Introduction / Context:
Combining non-collinear forces requires vector addition. When forces are perpendicular, the Pythagorean theorem directly gives the resultant magnitude. This appears frequently in statics and dynamics when resolving orthogonal components.

Given Data / Assumptions:

• Magnitudes: F1 = 6 N, F2 = 8 N.
• Right-angle between vectors.
• Planar force system.

Concept / Approach:

For perpendicular vectors A and B, |A + B| = √(A² + B²). This arises from the dot product with zero cross term since cos 90° = 0.

Step-by-Step Solution:

Verification / Alternative check:

Construct a 6-8-10 right triangle (a scaled 3-4-5 triangle), confirming the resultant magnitude is 10 N.

Why Other Options Are Wrong:

5 N and 7 N are too small; 12 N equals the arithmetic sum, not the vector sum; 8 N equals one component only.

Common Pitfalls:

Adding magnitudes arithmetically; forgetting that perpendicular components combine quadratically.

Final Answer:

10 N