Find the Scalar Product

Question

https://i.imgur.com/uHUjJXL.png

Answer 1

A=[2,-1,1], B=[1,2,-3];

2A=[4,-2,2], 2B=[2,4,-6];

2A+B=[5,0,-1], A-2B=[0,-5,7].

If dot product:

(2A+B)᛫(A-2B)=0+0-7=-7.

|-7|=7.

If vector product:

(2A+B)᰽(A-2B)=[0-(-1)(-5),-(5)(7)+0,(5)(-5)-0]=[-5,-35,-25].

|[-5,-35,-25]|=√(5²+35²+25²)=√1875=25√3=43.3 approx.