Linear Algebra · Lesson 2
Dot Product & Angle Between Vectors
The dot product is the fundamental way to measure how much two vectors "agree" in direction. It connects vector geometry to angle measurement and underlies projections, physics work calculations, and neural network activations.
Quick Check
1. What is (3, 4) · (1, 2)?
5
11
7
14
2. Two vectors are orthogonal when their dot product equals:
1
0
−1
∞
3. u · v = 10, ‖u‖ = 2, ‖v‖ = 5. The angle between them is:
45°
0° (parallel)
90°
60°
4. For any vector v, v · v equals:
‖v‖
‖v‖²
2‖v‖
0