Relative to a fixed origin OOO, the point A A\,A has position vector (i+6j+4k)(\mathbf{i} + 6\mathbf{j} + 4\mathbf{k})(i+6j+4k), the point B B\,B has position vector (−2i+3j+k)(-2\mathbf{i} + 3\mathbf{j} + \mathbf{k})(−2i+3j+k), and the point C C\,C has position vector (2i+5j+ak)(2\mathbf{i} + 5\mathbf{j} + a\mathbf{k})(2i+5j+ak), where a a\,a is a constant and a>4a > 4a>4. D D\,D is the point such that AB⃗=BD⃗\vec{AB} = \vec{BD}AB=BD.
Find the position vector of DDD.
Given that ∣AC⃗∣=11|\vec{AC}| = \sqrt{11}∣AC∣=11, find the value of aaa.
