Vector Addition and Scalar Multiplication

Vector Addition and Scalar Multiplication

This lesson covers the following key concepts:

• Triangle law of vector addition
• Parallelogram law of vector addition
• Polygon law of vector addition
• Properties of vector addition: commutative, associative
• Scalar multiplication and its properties
• Section formula for vectors (internal and external division)

Important Formulas

• $$a + b = (a₁ + b₁)i + (a₂ + b₂)j + (a₃ + b₃)k$$
• $$λa = (λa₁)i + (λa₂)j + (λa₃)k$$
• $$Section formula (internal): r = (mb + na)/(m + n)$$
• $$Section formula (external): r = (mb - na)/(m - n)$$
• $$Midpoint: r = (a + b)/2$$