The point A A\,A has the position vector (ab2)\begin{pmatrix} a \\ b \\ 2 \end{pmatrix}ab2 where a a\,a and b b\,b are positive constants, point B B\,B has the position vector (533)\begin{pmatrix} 5 \\ 3 \\ 3 \end{pmatrix}533 and point C C\,C has the position vector (311)\begin{pmatrix} 3 \\ 1 \\ 1 \end{pmatrix}311. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=6a + b = 6a+b=6
Given that the area of ABC ABC\,ABC is 363\sqrt{6}36, find the exact values of a a\,a and bbb.
