Case 1
- Vector A — x
- 1
- Vector A — y
- 2
- Vector A — z
- 3
- Vector B — x
- 4
- Vector B — y
- 5
- Vector B — z
- 6
32.0000
Open with these valuesDot Product Calculator
32.0000
Result: 32.0000Multiply the matching components and add the three products: (1, 2, 3) · (4, 5, 6) = 4 + 10 + 18 = 32. The answer is a single number, not a vector. Zero means the two vectors meet at a right angle, and a negative value means they point broadly opposite ways.
The numbers at a glance
Held fixed: Vector A — x 1.0000, Vector A — y 2.0000, Vector A — z 3.0000, Vector B — x 4.0000, Vector B — y 5.0000.
| Vector B — z | Result |
|---|---|
| 0.0000 | 14.0000 |
| 2.0000 | 20.0000 |
| 4.0000 | 26.0000 |
| 6.0000Your value | 32.0000 |
| 8.0000 | 38.0000 |
| 10.0000 | 44.0000 |
| 12.0000 | 50.0000 |
Worked examples
Case 2
- Vector A — x
- 1
- Vector A — y
- 0
- Vector A — z
- 0
- Vector B — x
- 0
- Vector B — y
- 1
- Vector B — z
- 0
0.0000
Open with these valuesCase 3
- Vector A — x
- -1
- Vector A — y
- 2
- Vector A — z
- -3
- Vector B — x
- 4
- Vector B — y
- -5
- Vector B — z
- 6
-32.0000
Open with these valuesHow it's calculated
A · B = ax·bx + ay·by + az·bz
- StepEnter the three components of vector A, then those of vector B.
- StepMatching components are multiplied: ax·bx, ay·by, az·bz.
- ResultThe three products are added into one number.
Reference table
| ax, ay, az, bx, by, bz | Products | Dot product |
|---|---|---|
| -1, 2, -3, 4, -5, 6 | −4 − 10 − 18 | -32.0000 |
| 1, 0, 0, 0, 1, 0 | 0 + 0 + 0 | 0.0000 |
| 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 | 0.04 + 0.1 + 0.18 | 0.3200 |
| 1.5, 2.5, 3.5, 2, 2, 2 | 3 + 5 + 7 | 15.0000 |
| 1, 2, 3, 4, 5, 6 | 4 + 10 + 18 | 32.0000 |
| 2, 3, 4, 5, 6, 7 | 10 + 18 + 28 | 56.0000 |
Questions
How do I calculate the dot product of two vectors?
Multiply the matching components of the two vectors and add the products: A · B = ax·bx + ay·by + az·bz. For (1, 2, 3) and (4, 5, 6) that is 4 + 10 + 18 = 32.
What is the dot product?
The dot product, also called the scalar product, takes two vectors and returns a single number rather than another vector. It measures how much the two vectors point the same way and is used for projections, the work done by a force, and angles.
What does a dot product of zero mean?
It means the two vectors are perpendicular — the angle between them is 90°. This follows from A · B = |A| |B| cos θ, because cos 90° is zero.
What is the difference between the dot product and the cross product?
The dot product returns a scalar and tells you how aligned two vectors are; the cross product returns a vector perpendicular to both. Use the dot product for angles and projections, the cross product for a perpendicular direction or an area.
Can the dot product be negative?
Yes. It is negative when the angle between the vectors is greater than 90°, so they point in broadly opposing directions. A positive result means they point the same way, and zero means they are perpendicular.
Sources and last check
Information, not professional advice.