Question Number 129804 by bramlexs22 last updated on 19/Jan/21
$$\mathrm{If}\:\overset{\rightarrow} {{p}}=\mathrm{2}\hat {{i}}+\mathrm{5}\hat {{j}}+\mathrm{6}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{q}}=\mathrm{3}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{8}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{r}}=\mathrm{2}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{10}\hat {{k}}\: \\ $$$$\:\mathrm{find}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{q}}×\overset{\rightarrow} {{r}}\:? \\ $$
Answered by EDWIN88 last updated on 20/Jan/21
$$\:\overset{\rightarrow} {\mathrm{p}}×\overset{\rightarrow} {\mathrm{q}}=\begin{vmatrix}{\mathrm{2}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\mathrm{6}}\\{\mathrm{3}\:\:\:\:\:\mathrm{6}\:\:\:\:\:\:\:\mathrm{8}}\end{vmatrix}=\:\mathrm{4}\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{3}\hat {{k}} \\ $$$$\:\overset{\rightarrow} {\mathrm{p}}×\overset{\rightarrow} {\mathrm{q}}×\overset{\rightarrow} {\mathrm{r}}=\:\begin{vmatrix}{\mathrm{4}\:\:\:\:\:\:\mathrm{2}\:\:\:\:−\mathrm{3}}\\{\mathrm{2}\:\:\:\:\:\:\mathrm{6}\:\:\:\:\:\mathrm{10}}\end{vmatrix}=\mathrm{38}\hat {{i}}−\mathrm{46}\hat {{j}}+\mathrm{20}\hat {{k}}\: \\ $$