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Question Number 129804 by bramlexs22 last updated on 19/Jan/21

If p^→ =2i^� +5j^� +6k^�      q^→ =3i^� +6j^� +8k^�      r^→ =2i^� +6j^� +10k^�     find p^→ ×q^→ ×r^→  ?

$$\mathrm{If}\:\overset{\rightarrow} {{p}}=\mathrm{2}\hat {{i}}+\mathrm{5}\hat {{j}}+\mathrm{6}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{q}}=\mathrm{3}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{8}\hat {{k}} \\ $$$$\:\:\:\overset{\rightarrow} {{r}}=\mathrm{2}\hat {{i}}+\mathrm{6}\hat {{j}}+\mathrm{10}\hat {{k}}\: \\ $$$$\:\mathrm{find}\:\overset{\rightarrow} {{p}}×\overset{\rightarrow} {{q}}×\overset{\rightarrow} {{r}}\:? \\ $$

Answered by EDWIN88 last updated on 20/Jan/21

 p^→ ×q^→ = determinant (((2     5       6)),((3     6       8)))= 4i^� +2j^� −3k^�    p^→ ×q^→ ×r^→ =  determinant (((4      2    −3)),((2      6     10)))=38i^� −46j^� +20k^�

$$\:\overset{\rightarrow} {\mathrm{p}}×\overset{\rightarrow} {\mathrm{q}}=\begin{vmatrix}{\mathrm{2}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\mathrm{6}}\\{\mathrm{3}\:\:\:\:\:\mathrm{6}\:\:\:\:\:\:\:\mathrm{8}}\end{vmatrix}=\:\mathrm{4}\hat {{i}}+\mathrm{2}\hat {{j}}−\mathrm{3}\hat {{k}} \\ $$$$\:\overset{\rightarrow} {\mathrm{p}}×\overset{\rightarrow} {\mathrm{q}}×\overset{\rightarrow} {\mathrm{r}}=\:\begin{vmatrix}{\mathrm{4}\:\:\:\:\:\:\mathrm{2}\:\:\:\:−\mathrm{3}}\\{\mathrm{2}\:\:\:\:\:\:\mathrm{6}\:\:\:\:\:\mathrm{10}}\end{vmatrix}=\mathrm{38}\hat {{i}}−\mathrm{46}\hat {{j}}+\mathrm{20}\hat {{k}}\: \\ $$

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