Parametric, Polar & Vectors · Vector Operations
Angle Between Vectors
The angle between two vectors is found using the dot product divided by the product of their magnitudes.
- 4 variables
- 2 worked examples
- 12 in Parametric, Polar & Vectors
Variables
| Symbol | Name | Unit |
|---|---|---|
| u1 | u x-component | - |
| u2 | u y-component | - |
| v1 | v x-component | - |
| v2 | v y-component | - |
Worked examples
- u · v = 1. |u| = 1, |v| = √2.
- cos θ = 1/√2 → θ = π/4 = 45°
Answer: π/4 (45°)
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Common questions
What is the Angle Between Vectors?
The angle between two vectors is found using the dot product divided by the product of their magnitudes. It is one of the parametric, polar & vectors formulas in the CalcRef reference.
What do the symbols in the Angle Between Vectors mean?
In the Angle Between Vectors, u1 is the u x-component; u2 is the u y-component; v1 is the v x-component; v2 is the v y-component.
How do you use the Angle Between Vectors?
Worked example. Find the angle between ⟨1, 0⟩ and ⟨1, 1⟩. u · v = 1. |u| = 1, |v| = √2. cos θ = 1/√2 → θ = π/4 = 45°. Answer: π/4 (45°).
Practice
Quiz yourself on Parametric, Polar & Vectors
Angle Between Vectors is one of 12 Parametric, Polar & Vectors formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.