Question Number 127566 by Ar Brandon last updated on 30/Dec/20
Answered by bramlexs22 last updated on 30/Dec/20
![(a^→ +b^→ )×(a^→ −b^→ )=a^→ ×a^→ −a^→ ×b^→ +b^→ ×a^→ −b^→ ×b^→ [ a^→ ×a^→ = 0 ; a^→ ×b^→ =−b^→ ×a^→ ] = 0 + 2(b^→ ×a^→ )−0 = 2(b^→ ×a^→ )](https://www.tinkutara.com/question/Q127573.png)
$$\left(\overset{\rightarrow} {\mathrm{a}}+\overset{\rightarrow} {\mathrm{b}}\right)×\left(\overset{\rightarrow} {\mathrm{a}}−\overset{\rightarrow} {\mathrm{b}}\right)=\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{a}}−\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}+\overset{\rightarrow} {\mathrm{b}}×\overset{\rightarrow} {\mathrm{a}}−\overset{\rightarrow} {\mathrm{b}}×\overset{\rightarrow} {\mathrm{b}} \\ $$$$\left[\:\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{a}}\:=\:\mathrm{0}\:;\:\overset{\rightarrow} {\mathrm{a}}×\overset{\rightarrow} {\mathrm{b}}=−\overset{\rightarrow} {\mathrm{b}}×\overset{\rightarrow} {\mathrm{a}}\:\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{0}\:+\:\mathrm{2}\left(\overset{\rightarrow} {\mathrm{b}}×\overset{\rightarrow} {\mathrm{a}}\right)−\mathrm{0}\:=\:\mathrm{2}\left(\overset{\rightarrow} {\mathrm{b}}×\overset{\rightarrow} {\mathrm{a}}\right)\: \\ $$
Commented by Ar Brandon last updated on 31/Dec/20
Thanks