Vector Addition and Subtraction Methods Quiz

Vector Addition Methods

• There are two methods to add vectors: Graphical Methods and Algebraic Methods (also referred to as component method)
• Graphical Methods involve the use of scale drawings, such as the polygon method

Graphical Methods

• For vectors in one dimension, simple addition and subtraction are used, with attention to signs
• For vectors in two dimensions, the Pythagorean Theorem can be used to find the displacement
• The parallelogram method can also be used, with vectors added "tail-to-tip"

Vector Properties

• The associative property of addition states that A + (B + C) = (A + B) + C
• The commutative law of addition states that A + B = B + A

Subtraction of Vectors

• To subtract vectors, the negative of a vector is defined, which has the same magnitude but points in the opposite direction
• Then, the negative vector is added to the original vector

Multiplication of a Vector by a Scalar

• A vector V can be multiplied by a scalar c, resulting in a vector cV with the same direction but a magnitude cV
• If c is negative, the resultant vector points in the opposite direction

Adding Vectors by Components

• To add vectors by components, one must:
  • Draw a diagram and add the vectors graphically
  • Choose x and y axes
  • Resolve each vector into x and y components
  • Calculate each component using sines and cosines
  • Add the components in each direction
  • Use the length and direction of the vector to find the final result

Unit Vectors

• A unit vector is a vector with a magnitude of exactly 1 and drawn in the direction of a given vector
• It lacks dimension and unit, and its only purpose is to specify a direction in space
• A given vector can be expressed as a product of its magnitude and a unit vector: 𝐴⃗ = 𝐴