Question Number 120258 by bramlexs22 last updated on 30/Oct/20
Answered by TANMAY PANACEA last updated on 30/Oct/20
$$\overset{\rightarrow} {{p}}={pcosa}\:{i}+{psina}\:{j} \\ $$$$\overset{\rightarrow} {{q}}={qcosb}\:{i}−{qsinb}\:{j} \\ $$$$\overset{\rightarrow} {{p}}.\overset{\rightarrow} {{q}}=\left({pcosa}\:{i}+{psina}\:{j}\right).\left({qcosb}\:{i}−{qsinb}\:{j}\right) \\ $$$${pqcosacosb}\:\left({i}.{i}\right)−{pqcosasinb}\:{i}.{j}+{pqsincosbj}.{i}−{pqsinasinb}\:\left({j}.{j}\right) \\ $$$${i}.{i}=\mathrm{1}\:\:\:{j}.{j}=\mathrm{1}\:\:\:{i}.{j}=\mathrm{0}\:\:\:{j}.{i}=\mathrm{0}\:\: \\ $$$$={pq}\left({cosacosb}−{sinasinb}\right) \\ $$$${again} \\ $$$$\overset{\rightarrow} {{p}}.\overset{\rightarrow} {{q}}={pqcos}\left({a}+{b}\right) \\ $$$${so}\: \\ $$$${pqcos}\left({a}+{b}\right)={pa}\left({cosacosb}−{sinasinb}\right) \\ $$$${cos}\left({a}+{b}\right)={cosacosb}−{sinasinb} \\ $$