## Calculus (3rd Edition)

$$v\times i =cj-bk$$ $$v\times j= -ci+ak.$$ $$v\times k= bi-aj.$$
First, we can write $$v=ai+bj+ck.$$ Now, we have $$v\times i=(ai+bj+ck)\times i\\ =a i\times i+b j\times i+c k\times i\\ =-bk+cj=cj-bk$$ $$v\times j=(ai+bj+ck)\times j\\ =a i\times j+b j\times j+c k\times j\\ =ak-ci=-ci+ak.$$ $$v\times k=(ai+bj+ck)\times k\\ =a i\times k+b j\times k+c k\times k\\ =-aj+bi=bi-aj.$$