3.7.2—Vector operations

Add and subtract vectors componentwise, multiply by a scalar to change magnitude or reverse direction, and use the dot product a·b=|a||b|cosθ to test perpendicularity.

A zero vector has no direction; scalar multiples are parallel. Keep dimensions and coordinate order consistent in every operation.

(2,−1)+(−3,4)=(−1,3); vectors are perpendicular when their dot product is zero.

The dot product is a scalar, not a vector, and a negative scalar reverses direction rather than merely reducing length.