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Multiplies
the *i*th
component of each vector together, then takes the sum.

Note that the dot product is a scalar.

**Example:** What
is the dot product of vectors **p** = [3, 2, 1]T and **q** = [1, 0, -1]T?

(3)(1) + (2)(0) + (1)(-1) = 2

Dot product - geometric interpretation

Dot
product is equivalent to:

Special case: if p · q = 0, the two vectors are*orthogonal*. This means they are perpendicular.

The sign of the dot product tells us whether to the vectors lie on the same side or on opposite sides of a plane.

**Example: **Find
the angle α between vectors p =
[1, 0, 0]T and q = [0, 0, 1]T.

Note: these vectors are orthogonal since the dot product is zero.

Note that the dot product is a scalar.

(3)(1) + (2)(0) + (1)(-1) = 2

Dot product - geometric interpretation

Special case: if p · q = 0, the two vectors are

The sign of the dot product tells us whether to the vectors lie on the same side or on opposite sides of a plane.

Note: these vectors are orthogonal since the dot product is zero.

High

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