A(2, 3, 1), B(-2, 2, 0) and C(0, 1, -1) are the vertices of the triangle ABC. Show that the triangle ABC is right -angled.

If A(1, 4, 2), B(-2, 1, 2) and C(2, -3, 4) are the vertices of the triangle ABC, then find the angles of the triangle ABC.

If A (-1, 4,2), B(3, -2, 0) and C(1,2,4) are the vertices of the triangle ABC, then the length of its median through the vertex A is-

Let A(0,beta), B(-2,0) and C(1,1) be the vertices of a triangle. Then Angle A of the triangle ABC will be obtuse if beta lies in

Let A(ct_(1), (c)/(t_(1))), B(ct_(2),(c)/(t_(2))) and C(ct_(3),(c)/(t_(3))) be the vertices of the triangle ABC. Show that the ortocentre of the triangle lies on xy=c^(2) .

Let A(0,beta), B(-2,0) and C(1,1) be the vertices of a triangle. Then All the values of beta for which angle A of triangle ABC is largest lie in the interval

If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

A(1,3,0),B(2,2,1) and C(5,-1,4) are the vertices of the triangle ABC, if the bisector of /_BAC meets its side bar(BC) at D, then find the coordinates of D.

The points (0,8/3),(1,3) and (82 ,30) are the vertices of (A) an obtuse-angled triangle (B) an acute-angled triangle (C) a right-angled triangle (D) none of these

In triangle ABC, If cos B= a/(2c) , then the triangle is-

Show that the points A=(2,-1,1),B=(1,-3,-5) and C=(3,-4,-4) are vertices of a right angled triangle (using vector method).