Question

If `A= <-8 ,3 ,-4 >` and `B= <-3 ,4 ,8 >`, what is `A*B -||A|| ||B||`?

Answer 1

`A*B-||A||||B||=-85`

Explanation:

Given vectors `vecu=u_x hati+u_yhatj+u_zhatk` and `vecv=v_xhati+v_yhatj+v_zhatk`, `u*v=u_xv_x+u_yv_y+u_zv_z` and `||u||=sqrt(u_x^2+u_y^2+u_z^2)`.
`A*B=(-8)(-3)+(3)(4)+(-4)(8)=4`
`||A||=sqrt((-8)^2+(3)^2+(-4)^2)=sqrt89`
`||B||=sqrt((-3)^2+(4)^2+(8)^2)=sqrt89`
`:.A*B-||A||||B||=4-sqrt89sqrt89=4-89=-85`