The points `A(x,y), B(y, z)` and C(z,x) represents the vertices of a right angled triangle, if

If the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then

If the points A(3,4),B(x_1 ,y _1) and C(x_2 ,y_2) are such that both 3 , x_1, x_2 and 4, y_1 ,y_2 are in AP, then (i) A , B , C are vertices of an isosceles triangle (ii) A , B , C are collinear points (iii) A , B , C are vertices of a right angle triangle (iv) A , B , C are vertices of a scalene triangle (v) A , B , C are vertices of a equilateral triangle

If the points A(x,y+z),B(y,z+x) and "C(z,x+y)" are such that AB=BC ,then x,y,z are in A .P

suppose that the mid point of the sides BC,CA and AB of a triangle Delta ABC are (5,7,11), (0,8,5) and (2,3,-1) If the vertices of the triangle are A(x_1,y_1,z_1), B(x_2,y_2,z_2) and C(x_3,y_3,z_3) derive nine equations in x_1,x_2,x_3,y_1,y_2,y_3,z_1,z_2, and z_3

A(z_a), B(z_b), C(z_c) are vertices of right angled triangle, zc being the orthocentre. A circle is described on AC as di- ameter. Find the point of intersection of the circle with hypotenuse.

The triangle formed by joining the points (x,y,z), (y,z,x) and (z,x,y) in three dimensional space is-

Does (a)/(x-y)+(b)/(y-z)+(c)/(z-x)=0 represents a pair of planes?

Does (a)/(x-y)+(b)/(y-z)+(c)/(z-x)=0 represents a pair of planes?

Does (a)/(x-y)+(b)/(y-z)+(c)/(z-x)=0 represents a pair of planes?

Does (a)/(x-y)+(b)/(y-z)+(c)/(z-x)=0 represents a pair of planes?