If `A ,\ B ,\ C` have position vectors (0, 1, 1), (3, 1, 5), (0, 3, 3) respectively, show that `"Delta"A B C` is right angled at `Cdot`

If A ,B ,C have position vectors (2,0,0),(0,1,0),(0,0,2), show that A B C is isosceles.

If the vertices A, B, C of a triangle ABC are (1, 2, 3), (1, 0, 0), (0, 1, 2) , respectively, then find /_A B C . [ /_A B C is the angle between the vectors vec( B A) and vec (B C) .

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

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

Show that the points A(0,1,2),B(2,-1,3)a n dC(1,-3,1) are vertices of an isosceles right-angled triangle.

The values of a for which the points A,B,C with position vectors 2hati+hatj+hatk, hati-3hatj-5hatk and ahati-3hatj+hatk respectively are the vertices of a righat angled triangle at C are (A) 2 and 1 (B) -2 and -1 (C) -2 and 1 (D) 2 and -1

The values of a for which the points A, B, and C with position vectors 2hati - hatj + hatk, hati - 3hatj - 5hatk, and ahati - 3hatj + hatk ,respectively, are the vertices of a right-angled triangle with C = pi/2 are

Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.

If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2), respectively then find /_A B Cdot

Show that the points A,B and C having position vectors (3hati - 4hatj - 4hatk), (2hati - hatj + hatk) and (hati - 3hatj - 5hatk) respectively, from the vertices of a right-angled triangle.