component of each vector together, then takes the sum.
that the dot product is a scalar.Example:
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
product is equivalent to:
case: if p · q = 0, the two
vectors are orthogonal
. This means they are perpendicular.
sign of the dot product tells us whether to the vectors lie on the same side or on opposite sides of a plane.Example:
the angle α between vectors p =
[1, 0, 0]T and q = [0, 0, 1]T.
these vectors are orthogonal since the dot product is zero.