If A= <7 ,-5 ,1 >A=<7,5,1> and B= <28 ,6 ,7 >B=<28,6,7>, what is A*B -||A|| ||B||AB||A||||B||?

1 Answer
May 2, 2017

173-5sqrt(2607)17352607

Explanation:

For a vector vec X=((x_1),(x_2),(x_3)), its magnitude is ||vec X||=sqrt(x_1^2+x_2^2+x_3^2). For two vectors vec X=((x_1),(x_2),(x_3)) and vec Y=((y_1),(y_2),(y_3)), their dot product is vec X*vec Y=x_1y_1+x_2y_2+x_3y_3.

From the above, vec A*vec B=7*28+ -5*6+1*7=173. The magnitude of vec A=||vec A||=sqrt(7^2+(-5)^2+1^2)=sqrt(75)=5sqrt(3). The magnitude of vec B=||vec B||=sqrt(28^2+6^2+7^2)=sqrt(869).

Therefore, vec A*vec B-||vec A||||vec B||=173-5sqrt(3)sqrt(869)=173-5sqrt(2607).