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 (143)\begin{pmatrix} 1 \\ 4 \\ 3 \end{pmatrix}143 and point C C\,C has the position vector (361)\begin{pmatrix} 3 \\ 6 \\ 1 \end{pmatrix}361. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=7a + b = 7a+b=7
Given that the area of ABC ABC\,ABC is 262\sqrt{6}26, find the exact values of a a\,a and bbb.
