Given:
Two vertices of a triangle are (3, -2) and (-2, 3) and its orthocentre is (-6, 1).

To find:
The coordinates of the third vertex of the triangle.

Solution:
We know that the orthocentre of a triangle is the point of intersection of its altitudes. Therefore, we need to find the equation of two altitudes passing through the given vertices.

Altitude from (3, -2):
The slope of the line joining (3, -2) and (-2, 3) is (3 - (-2))/(3 - (-2)) = 1.
Therefore, the slope of the line perpendicular to this line is -1.
The equation of the line passing through (3, -2) with slope -1 is y + 2 = -1(x - 3) or x + y - 1 = 0.
The foot of the altitude from (-6, 1) to this line lies on this line.
Let the foot of the altitude from (-6, 1) to this line be (a, b).
Then, the slope of the line passing through (-6, 1) and (a, b) is -1/(-1) = 1.
Therefore, (b - 1)/(a + 6) = 1 or b - a - 5 = 0.
Also, (a, b) lies on the line x + y - 1 = 0.
Solving these two equations, we get a = -1 and b = 6.

Therefore, the foot of the altitude from (-6, 1) to the line passing through (3, -2) is (-1, 6).

Altitude from (-2, 3):
Similarly, the slope of the line joining (-2, 3) and (3, -2) is (3 - (-2))/(-2 - 3) = -1.
Therefore, the slope of the line perpendicular to this line is 1.
The equation of the line passing through (-2, 3) with slope 1 is y - 3 = 1(x + 2) or x - y + 1 = 0.
The foot of the altitude from (-6, 1) to this line lies on this line.
Let the foot of the altitude from (-6, 1) to this line be (c, d).
Then, the slope of the line passing through (-6, 1) and (c, d) is -1/1 = -1.
Therefore, (d - 1)/(c + 6) = -1 or d + c + 7 = 0.
Also, (c, d) lies on the line x - y + 1 = 0.
Solving these two equations, we get c = -1 and d = -6.

Therefore, the foot of the altitude from (-6, 1) to the line passing through (-2, 3) is (-1, -6).

The third vertex of the triangle is the point of intersection of the altitudes passing through (3, -2) and (-2, 3).
The equation of the line passing through these two points is x + y = 1.
The coordinates of the foot of the altitude from the third vertex to this line can be obtained by solving the