# The points with position vectors $60\hat i+3\hat j,\:70\hat i-8\hat j\:and\:a\hat i-52\hat j$ are collinear if $a=?$

$\begin{array}{1 1} 40 \\ -40 \\ 80 \\ -80 \end{array}$

Let the points be $A(60\hat i+3\hat j),\:B(40\hat i-8\hat j) \:and\:C(a\hat i-52\hat j)$
$\overrightarrow {AB}=-20\hat i-11\hat j$
$\overrightarrow {BC}=(a-40)\hat i-44\hat j$
If $A,B,C$ are collinear, then $\overrightarrow {AB}=\lambda \overrightarrow {BC}$
for some constant $\lambda$
$\Rightarrow\:-80=a-40$
$\Rightarrow\:a=-40$