Module 2: The Dot Product
Let x=(x1,x2,…,xn) and
y=(y1,y2,…,yn) be two vectors in
Rn. Then the dot product of
x and
y is:
x⋅y=x1y1+x2y2+⋯+xnyn=∑nk=1xkyk.
It is important to note that the dot product of two vectors is a real number (and not a vector)!
Examples:
1. Let x=(1,2) and
y=(−1,4). Then
x⋅y=(1,2)⋅(−1,4)=1⋅−1+2⋅4=−1+8=7.
2. Let x=(1,2,−1) and
y=(−1,−2,t). Find all values of
t which make
x⋅y=0.
x⋅y=−1−4−t=0⇒t=−5.