Vectors
Start your linear algebra journey here with vectors as shifts in space.
Vectors
Vector Addition
Drawing Vectors
Component-Wise Addition
Level Check
Opposite Vectors
Vector Subtraction
Drawing Differences
Vector Differences
Level Check
Scalar Multiplication
Reversing Direction
Linear Combinations
Linear Combination Grids
Solving Linear Combinations
Drawing Linear Combinations
Linear Interpolation
Magnitude and Direction
Drawing from Polar Form
Polar Angles
Finding the Polar Angle
Computing from Components
Vector Components
Non-Polar Angles
Combining Vectors
Adding Velocities
Velocity Magnitude and Direction
Velocity from Bearing
Combining Velocity Bearings
Relative Velocity
Scaling and Magnitude
Unit Vectors
Comparing Unit Vectors
The Dot Product
Unit Vector Dot Products
General Dot Products
Scaling Dot Products
Dot Product from Magnitudes
Angle from Dot Product
Self Dot Products
Orthogonal Dot Products
Course description
Explore vectors as shifts in space, using grids and arrows to build intuition before any formulas appear. By the end of the course, you'll be able to add, subtract, and scale vectors, describe them by magnitude and direction, combine velocities and bearings, and measure how much two vectors point the same way with the dot product. You'll see where each operation comes from geometrically rather than just applying a rule.
Topics covered
- Bearings
- Dot Products
- Inverse Tangent
- Linear Combinations
- Linear Interpolation
- Magnitude and Direction
- Relative Velocity
- Scalar Multiplication
- Unit Vectors
- Vector Addition
- Vector Components
- Vector Subtraction
Prerequisites and next steps
Before you get started, you should be comfortable with basic algebraic expressions and right-triangle trigonometry, since you'll use inverse tangent to find a vector's direction. You don't need any prior experience with vectors to begin. When you finish, the Matrices course picks up right where this one leaves off.