Let three toys A, B and C be placed in the same straight line. If the position vectors of A, B and C are $55\hat{i} - 2\hat{j}$, $5\hat{i} + 8\hat{j}$ and $a\hat{i} - 52\hat{j}$ respectively, find the exact numerical value of '$a$'.
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For 2D collinearity, you can also use the determinant of the coordinates set to zero: $\begin{vmatrix} x_1 & y_1 & 1 x_2 & y_2 & 1 x_3 & y_3 & 1 \end{vmatrix} = 0$. This avoids needing to compute separate vectors!