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))`

Find the scalar components and magnitude of the vector joining the points P(x_(1),y_(1),z_(1))andQ(x_(2),y_(2),z_(2)) .

The coordinates of any point on the line-segment joining the points ( x _(1) ,y_(1) , z_(1)) and (x_(2), y_(2),z_(2)) are ((x_(1)+kx_(2))/(k + 1),(y _(1) + ky_(2))/(k + 1),(z_(1)+kz_(2))/(k + 1)) , then the value of k will be _

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

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.

If (x_(1),y_(1),z_(1)) , (x_(2),y_(2),z_(2)) , (x_(3) ,y_(3),z_(3)) and (x_(4) , y_(4) , z_(4)) be the consecutive vertices of a parallelogram, show that x_(1)+x_(3)=x_(2)+x_(4),y_(1)+y_(3)=y_(2)+y_(4) and z_(1)+z_(3)=z_(2)+z_(4) .

The coordinates of the point where the line (x-3)/(1)=(y-4)/(2)=(z-5)/(2) meets the plane x+y+z=17 are -

The lines (x)/(1)=(y)/(2)=(z)/(3) and (x-1)/(-2)=(y-2)/(-4)=(3-z)/(6) are

Find the equation of the projection of the line (x-1)/(2)=(y+1)/(-1)=(z-3)/(4) on the plane x+2y+z=9 .

Find the value of x, y and z from the following equations: (i) [(4,3),(x,5)]=[(y,z),(1,5)] (ii) [(x+y, 2 ),(5+z, xy)]=[(6,2),(5,8)] (iii) [(x+y+z),(x+z), (y+z)]=[(9),(5),(7)]