Dot product
For vectors a and b, multiply matching entries and add. It is zero exactly when the vectors are at right angles, and it equals |a||b| cos(angle).
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Analogy
Measuring how much two people are pushing a box in the same direction.
Example
1 x 4 = 4.2 x (-5) = -10.3 x 6 = 18.Total 4 - 10 + 18 = 12.
In practice
Used to find angles, projections and work done by a force.
Practice
Flashcards
- What is (1, 2, 3) dot (4, -5, 6)?12.
- What does a zero dot product tell you?The two vectors are perpendicular.
Questions people ask
How do I use the dot product to find an angle?
Rearrange a dot b equals length of a times length of b times cos of the angle. So cos of the angle is the dot product divided by the two lengths. For (1, 0) and (1, 1), that is 1 over root 2, so 45 degrees.
What does a dot product of zero mean?
The two vectors are perpendicular (orthogonal), assuming neither is the zero vector. For example, (2, 1) dot (1, -2) is 2 minus 2, which is zero. This is a quick test for right angles in geometry and physics. It saves you from drawing the vectors or measuring any angle with a protractor.