Vectors

▶ Vector intro for linear algebra

A vector has both magnitude and direction. We use vectors to, for example, describe the velocity of moving objects. In this video, you'll learn how to write and draw vectors.

▶ Real coordinate spaces

▶ Adding vectors algebraically & graphically

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

▶ Multiplying a vector by a scalar

Watch Sal change the magnitude of a vector by multiplying it by a scalar.

▶ Vector examples

Visually understanding basic vector operations

▶ Unit vectors intro

Unit vectors are vectors whose magnitude is exactly 1 unit. They are very useful for different reasons. Specifically, the unit vectors [0,1] and [1,0] can form together any other vector.

▶ Parametric representations of lines

Parametric Representations of Lines in R2 and R3