3Blue1Brown: Vectors | Essence of Linear Algebra - Chapter 1 Quiz

Vectors: geometric and numerical reasoning

This quiz accompanies Chapter 1 of 3Blue1Brown’s Essence of Linear Algebra. It revisits vector interpretations, coordinates, addition, scaling and applications.

Practice

• Read coordinates in two and three dimensions.
• Connect arrows with ordered numerical components.
• Interpret addition as successive displacements.
• Apply scalar multiplication to every component.

For vectors in the same coordinate system, addition follows $$\begin{pmatrix}a\b\end{pmatrix}+\begin{pmatrix}c\d\end{pmatrix}=\begin{pmatrix}a+c\b+d\end{pmatrix}$$. Scaling follows $$k\begin{pmatrix}a\b\end{pmatrix}=\begin{pmatrix}ka\kb\end{pmatrix}$$. A negative factor reverses a nonzero vector’s direction.

Basic signed arithmetic and Cartesian coordinates are useful prerequisites. Work out the answer before reading the explanation, and compare the numerical calculation with a sketch. The quiz covers introductory vector ideas; it does not require determinants, eigenvalues or matrix inversion.