Vector Algebra: 3 marks Questions (CBSE Class 12)

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 value of ‘a’.

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are unit vectors, then prove that
$|\vec{a}-\vec{b}{|}^2+|\vec{b}-\vec{c}{|}^2+|\vec{c}-\vec{a}{|}^2\le 9$.