A particle is moving in an elliptical orbit as shown in figure. If  $\overrightarrow{p},\overrightarrow{L}$ and $\overrightarrow{r}$ denote the linear momentum, angular momentum and position vector of the particle (from focus O) respectively, when the particle is point at A, then the direction of $\overrightarrow{\alpha }=\overrightarrow{p}\times \overrightarrow{L}$  is along   

From figure, Linear momentum towards +ve y-axis  $\left(p\widehat{j}\right).$  
 From right hand thumb rule, Angular momentum  $\left(\overrightarrow{L}\right)$ is towards +ve z-axis  $\left(L\widehat{k}\right)$
 Now, 
 $\overrightarrow{\alpha }=\overrightarrow{p}\times \overrightarrow{L}=\left(p\widehat{j}\right)\times \left(L\widehat{k}\right)=pL(\widehat{j}\times \widehat{k})=pL\widehat{i}$
 From properties of cross product of 2 vectors, the direction of $\overrightarrow{\alpha }$  is along +ve x-axis.