Parametric, Polar & Vectors · Vector Operations
Dot Product
The dot product is a scalar equal to the sum of component products. It also equals the product of magnitudes times the cosine of the angle between them.
- 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
- (1)(4) + (2)(-5) + (3)(6) = 4 - 10 + 18 = 12
Answer: 12
1 more worked examplePremium
Step-by-step solution locked.
See all 12 Parametric, Polar & Vectors formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Common questions
What is the Dot Product?
The dot product is a scalar equal to the sum of component products. It also equals the product of magnitudes times the cosine of the angle between them. It is one of the parametric, polar & vectors formulas in the CalcRef reference.
What do the symbols in the Dot Product mean?
In the Dot Product, 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 Dot Product?
Worked example. Find ⟨1, 2, 3⟩ · ⟨4, -5, 6⟩. (1)(4) + (2)(-5) + (3)(6) = 4 - 10 + 18 = 12. Answer: 12.
Practice
Quiz yourself on Parametric, Polar & Vectors
Dot Product 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.