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 (114)\begin{pmatrix} 1 \\ 1 \\ 4 \end{pmatrix}114 and point C C\,C has the position vector (772)\begin{pmatrix} 7 \\ 7 \\ 2 \end{pmatrix}772. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=8a + b = 8a+b=8
Given that the area of ABC ABC\,ABC is 114\sqrt{114}114, find the exact values of a a\,a and bbb.
