3.7.6—Scalar product

For vectors a and b, a·b=|a||b|cosθ and in components a₁b₁+a₂b₂(+a₃b₃). A zero scalar product means perpendicular non-zero vectors.

Use the dot product to find an angle, a projection or a perpendicular condition. Check that the angle is the requested principal angle and that neither vector is zero.

(1,2)·(2,−1)=0, so the vectors are perpendicular; their magnitudes do not need to be equal.

The scalar product is not a vector and a negative value means an obtuse angle, not an impossible result.