Question Number 66980 by Mr Jor last updated on 21/Aug/19
Commented by Mr Jor last updated on 21/Aug/19
$${The}\:{figure}\:{above}\:{is}\:{a}\:{right}\:{pyramid} \\ $$$${with}\:{a}\:{rectangular}\:{base}\:{ABCD}\:{and} \\ $$$${VO}\:{as}\:{the}\:{height}. \\ $$$${The}\:{vectors}\:\boldsymbol{{AD}}=\boldsymbol{{a}},\boldsymbol{{AB}}=\boldsymbol{{b}}\:{and}\:\boldsymbol{{DV}}=\boldsymbol{{c}} \\ $$$${M}\:{is}\:{a}\:{point}\:{on}\:{OV}\:{such}\:{that}\:{OM}:{MV} \\ $$$$=\mathrm{3}:\mathrm{4}.{Express}\:\boldsymbol{{BM}}\:{in}\:{terms}\:{of}\:\boldsymbol{{a}}, \\ $$$$\boldsymbol{{b}}\:{and}\:\boldsymbol{{c}}.{Simplify}\:{your}\:{answer}\:{as} \\ $$$${far}\:{as}\:{possible}. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:{Ans}:\boldsymbol{{BM}}=\frac{\mathrm{5}}{\mathrm{7}}\boldsymbol{{a}}−\frac{\mathrm{5}}{\mathrm{7}}\boldsymbol{{b}}+\frac{\mathrm{3}}{\mathrm{7}}\boldsymbol{{c}} \\ $$