dot product and norm [closed]

Question

Can you solve the following problem in mathematica program? Thank you.

Let x=(x1,x2,x3),y=(y1,y2,y3) and ⟨x,y⟩=x1y1+2x2y2+x3y3 be an inner product in a three-dimensional real vector space.

Define the function that calculates the dot product of two vectors and calculate the dot product of the vectors (−1,1,2),(3,2,−1).

Define the function that calculates the norm of a vector obtained from this dot product and calculate the norm of the vector (−1,1,2),(3,2,−1).

Answer 1

x = {x1, x2, x3};
y = {y1, y2, y3};
Dot[x, y]

v1 = {-1, 1, 2}
v2 = {3, 2, -1}
Dot[v1, v2]
Norm[v1]
Norm[v2]
Norm[Dot[v1, v2]]