Write the coordinate of the centroid of the triangle whose vertices are
`(x_1,y_1,z_1)`,`(x_2,y_2,z_2)` and `(x_3,y_3,z_3)`

What are the coordinates of the centroid of the triangle with vertices (x_1,y_1) (x_2,y_2) and (x_3,y_3)

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

(b)The coordinates of the point R which divides the line segment joining P(x1,y1,z1) and Q(x2,y2,z2) internally in the ratio m:n are given by…………

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

A plane makes intercepts a, b, c at A, B, C on the coordinate axes respectively. If the centroid of the Delta ABC is at (3, 2, 1), then the equation of the plane is a) x + 2y + 3z = 9 b) 2x - 3y - 6z = 18 c) 2x + 3y + 6z = 18 d) 2x + y + 6z = 18

Find the equation of the plane through the point (1,2,3) and perpendicular to the plane x-y+z=2 and 2x+y-3z=5

If Q is the image of the point P (2,3,4) under the reflection in the plane x-2y+5z=6 then the equation of the line PQ is a) (x-2)/(-1)= (y-3)/2= (z-4)/5 b) (x-2)/(1)= (y-3)/(-2)= (z-4)/5 c) (x-2)/(-1)= (y-3)/(-2)= (z-4)/5 d) (x-2)/(1)= (y-3)/(2)= (z-4)/5

Examine the consistency of the system of equations 5 x-y+4z=5 , 2 x+3 y+5 z=2, 5 x-2 y+6 z=-1

Examine the consistency of the following system of equation 5x-y+4z=5 2x+3y+5z=2 5x -2y+6z =-1