Lecture: Unit Vector

Introduction

• Lecturer: Hazwan Yusof
• Topic: Unit Vector
• Definition: A unit vector is also known as a direction because it only shows the direction without any units like meters, newtons, kilograms.
• Symbol: Unit vector is written as U.

Basic Concepts

• A unit vector is the vector over the vector infection with the symbol U.
• The direction from point A to point B is written as Uab.

Example: Calculating Unit Vector

Steps

1. Determine the Coordinates of Points

   • Point A:
     • X: Positive 1 (moving towards positive 1 meter)
     • Y: 0 (no need to move)
     • Z: Negative 3 (moving down 3 meters)
   • Point B:
     • X: Negative 2 (moving back 2 meters)
     • Y: Positive 2 (moving right 2 meters)
     • Z: Positive 3 (moving up 3 meters)

2. Calculate Direction (RAB)

   • Use the formula: Coordinate B - Coordinate A
   • Example calculation:
     • I (X): B (-2) - A (1) = -3
     • J (Y): B (2) - A (0) = 2
     • K (Z): B (3) - A (-3) = 6
   • Result: RAB = -3I + 2J + 6K

3. Calculate Magnitude

   • Use the formula: Square root (x² + y² + z²)
   • Example: Square root (9 + 4 + 36) = 7 meters

4. Calculate Unit Vector

   • Formula: Vector / Magnitude
   • Example: (-3/7)I + (2/7)J + (6/7)K

Verification

• Magnitude of a Unit Vector: Always 1
• If the result of the magnitude calculation is 1, then the unit vector is correct.

Summary

• Make sure to use B - A for the direction from A to B.
• A unit vector is the vector divided by the magnitude.
• The magnitude of the unit vector is always 1.

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