The point A A\,A has the position vector (ab3)\begin{pmatrix} a \\ b \\ 3 \end{pmatrix}ab3 where a a\,a and b b\,b are positive constants, point B B\,B has the position vector (234)\begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}234 and point C C\,C has the position vector (012)\begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}012. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=3a + b = 3a+b=3
Given that the area of ABC ABC\,ABC is 8\sqrt{8}8, find the exact values of a a\,a and bbb.
