Question

If $\overline{a},\overline{b},\overline{c}$ are the position vectors of the points $A,B,C$ respectively, where $A\equiv (1,3,0),B\equiv (2,5,0),C\equiv (4,2,0)$ and $\overline{c}=x\overline{a}+y\overline{b}$, then find $x$ and $y$

Answer 1

Given: $\overline{c}=x\overline{a}+y\overline{b}$ -----(1)

Also, $\overline{c}=4i+2j,\overline{b}=2i+5j,\overline{a}=i+3j$

$4i+2j=x(i+3j)+y(2i+5j)\to x+2y=4,3x+5y=2$ ------by(1)

Solving both equations for $x$ and $y$,

we get $x=-16,y=10$