The co-ordinate of three vertices and centroid of a triangle are (x, 2, 3), (3, y, 5), (-1, 6, z) and (1,4,1/3). Find x, y, z

If the co-ordinate of three vertices of a- triangle are (9, 1, -3), (1.- 1, -5) and (3, 1, 3). Show that the triangle is equilateral

Find the co-ordinate of the orthocentre of a triangle whose vertices are A(-2,-3),B(6,1)and C(1,6).

The coordinates of the centroid of the triangle formed by joining the points ( x , -1, -2) , ( - 2 , y , 8) and ( 2 , - 4 , z) are (1 , 0 , 30 , find the values of x , y and z .

The coordinates of centroid of the trianle formed by joining the points (x,-1,-2),(-2,y,8) and (2,-4,z) are (1,0,3) find the values of x,y and z.

Find the coordinates of the centroid fof the triangle whose vertices are (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) and (x_(3),y_(3),z_(3))

(4, -3), (-5, 2) and (x, y) are the three vertices of a triangle. If the centroid of the triangle be the origen, find the values of x and y.

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

Vertices of /_\XYZ are X(-2, -3),Y (6, 1), and Z(1, 6). Find the co-ordinate of its orthocentre.

Find the value of each of the following polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vi) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

Find the ratio in which the plane 2x + 2y - 2z = 1 divides the line segment joining the points A(2,1, 5) and B(3, 4, 3). Find the co¬ ordinate of point of contact.