01 (f). Multiplication of Vectors - Dot Product - Vectors - Physics 101

Transcript

the dot product also known as the scalar product of two vectors is a scalar quantity that measures the projection of one vector onto other Vector this operation is denoted by Dot and it is calculated by multiplying the magnitude of one vector by the magnitude of other vector and then multiplying that by the cosine of the angle between them in other words the dot product measures how much two vectors are aligned with each other if p and Q are perpendicular to each other then their dot product is zero meaning they are completely unrelated if they are pointing in the same direction then their dot product is positive and if they are pointing in opposite directions their dot product is negative the dot product has several important properties first it is commutative meaning that P dot Q is equals to Q dot P second the dot product is distributive over vector addition meaning that P plus Q dot C is equals to P dot C plus Q dot C third the dot product is linear meaning that for any scalar k k time P dot Q is equals to K times P dot Q which is again equal to P dot k times Q