JEE Advance - Mathematics (1983 - No. 27)
The vertices of a triangle are
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.
$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3},a\left( {{t_2} + {t_3}} \right)} \right],\,\,\left[ {a{t_3}{t_1},\,a\left( {{t_3} + {t_1}} \right)} \right]$$. Find the orthocentre of the triangle.
$$\left( {a,a\left( {{t_1} + {t_2} + {t_3}} \right) - a{t_1}{t_2}{t_3}} \right)$$
$$\left( { - a,a\left( {{t_1} + {t_2} + {t_3}} \right) - a{t_1}{t_2}{t_3}} \right)$$
$$\left( {a,a\left( {{t_1} + {t_2} + {t_3}} \right) + a{t_1}{t_2}{t_3}} \right)$$
$$\left( { - a,a\left( {{t_1} + {t_2} + {t_3}} \right) + a{t_1}{t_2}{t_3}} \right)$$
$$\left( {0,a\left( {{t_1} + {t_2} + {t_3}} \right) + a{t_1}{t_2}{t_3}} \right)$$