Show that the triangle ABC with vertices A(0,4,1),B(2,3,-1) and C(4,5,0) is right angled.

Show that the triangle with vertices (0, 7, 10), (-1, 6, 6) and (- 4, 9, 6) is right-angled.

Show that the triangle with vertices (6, 10, 10), (1, 0, - 5) and (6, - 10, 0) is a right-angled triangle.

Using vectors find the area of the triange ABC with vertices A(1,2,3),B(2,-1,4) and C(4,5,-1).

Using vectors find the area of the triangle ABC with vertices A(1,0,3),B(2,1,4) and C(4,3,1).

If the origin is the centroid of triangle ABC, with vertices A(a,1,3), B(-2,b,-5) and C(4,7,c). Find the values of a,b and c.

In the triangle ABC with vertices A (2, 3), B (4,-1) and C (1, 2), find the equation and length of altitude from the vertex A.

Find the measure of the angle A of the triangle ABC with vertices A (2, 3), B (-2, 2) and C(0, 2).

The medians AD and BE of the triangle ABC with vertices A(0, b), B(0, 0) and C(a, 0) are mutually perpendicular if