Question Number 72832 by necxxx last updated on 03/Nov/19
$${In}\:{a}\:{parallelogram}\:{OABC},\:{O}\overset{\rightharpoondown} {{A}}=\overset{−\rightharpoondown} {{a}}, \\ $$$${O}\overset{\rightarrow} {{C}}=\overset{\rightarrow} {{c}},\:{D}\:{is}\:{a}\:{point}\:{such}\:{that}\:{A}\overset{\rightarrow} {{D}}:{D}\overset{\rightarrow} {{B}}=\mathrm{1}:\mathrm{2} \\ $$$${Express}\:{the}\:{following}\:{in}\:{terms}\:{of}\:{a}\:{and}\:{c} \\ $$$$\left({i}\right){C}\overset{\rightarrow} {{B}}\:\left({ii}\right){B}\overset{\rightarrow} {{C}}\:\left({iii}\right){A}\overset{\rightarrow} {{B}}\:\left({iv}\right)\:{A}\overset{\rightarrow} {{D}}\:\left({v}\right){O}\overset{\rightarrow} {{D}} \\ $$$$\left({vi}\right){D}\overset{\rightarrow} {{C}} \\ $$
Commented by necxxx last updated on 03/Nov/19
$${please}\:{help}.\:{Thanks}\:{in}\:{advance}. \\ $$
Answered by mind is power last updated on 03/Nov/19
$$\mathrm{C}\overset{\rightarrow} {\mathrm{B}}=\mathrm{O}\overset{\rightarrow} {\mathrm{A}}=\overset{\rightarrow} {\mathrm{a}} \\ $$$$\mathrm{B}\overset{\rightarrow} {\mathrm{C}}=−\mathrm{C}\overset{\rightarrow} {\mathrm{B}}=−\overset{\rightarrow} {\mathrm{a}} \\ $$$$\mathrm{A}\overset{\rightarrow} {\mathrm{B}}=\mathrm{O}\overset{\rightarrow} {\mathrm{C}}=\overset{\rightarrow} {\mathrm{c}} \\ $$$$\mathrm{A}\overset{\rightarrow} {\mathrm{D}}=\frac{\mathrm{1}}{\mathrm{2}}.\mathrm{D}\overset{\rightarrow} {\mathrm{B}} \\ $$$$\mathrm{A}\overset{\rightarrow} {\mathrm{D}}+\mathrm{D}\overset{\rightarrow} {\mathrm{B}}=\mathrm{A}\overset{\rightarrow} {\mathrm{B}} \\ $$$$\mathrm{3A}\overset{\rightarrow} {\mathrm{D}}=\mathrm{A}\overset{\rightarrow} {\mathrm{B}}\Rightarrow\mathrm{A}\overset{\rightarrow} {\mathrm{D}}=\frac{\mathrm{A}\overset{\rightarrow} {\mathrm{B}}}{\mathrm{3}}=\frac{\overset{\rightarrow} {\mathrm{c}}}{\mathrm{3}} \\ $$$$\mathrm{O}\overset{\rightarrow} {\mathrm{D}}=\mathrm{O}\overset{\rightarrow} {\mathrm{A}}+\mathrm{A}\overset{\rightarrow} {\mathrm{D}}=\overset{\rightarrow} {\mathrm{a}}+\frac{\overset{\rightarrow} {\mathrm{c}}}{\mathrm{3}} \\ $$
Commented by necxxx last updated on 03/Nov/19
$${I}\:{now}\:{get}\:{it}.\:{Thank}\:{you}\:{so}\:{much}\:{sir} \\ $$