A tetahedron is a three dimensional figure bounded by forunon coplanar trianglular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates `(x_1,y_1,z_1)(x_2,y_2,zs_2),(x_3,y_3,z_3) and (x_4,y_4,z_4)` respectivley in a rectngular three dimensionl space. Then the coordinates of tis centroid are `(x_1+x_2+x_3+x4)/4, (y_1+y_2+y_3+y_4)/4, (z_1+z_2+z_3+z_4)/4`. the circumcentre of the tetrahedron is th centre of a sphere pssing thorugh its vetices. So, this is a point equidistasnt from each ofhate vertices fo the tetrahedron. Let a tetrahedron hve three of its vertices reresented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centrod lies at the point (1,2,5). THe coordinate of the fourth vertex of the tetrahedron is

A tetahedron is a three dimensional figure bounded by forunon coplanar trianglular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates (x_1,y_1,z_1)(x_2,y_2,zs_2),(x_3,y_3,z_3) and (x_4,y_4,z_4) respectivley in a rectngular three dimensionl space. Then the coordinates of tis centroid are (x_1+x_2+x_3+x4)/4, (y_1+y_2+y_3+4)/4, (z_1+z_2+z_3+z_4)/4 . the circumcentre of the tetrahedron is th centre of a sphere pssing thorugh its vetices. So, this is a point equidistasnt from each ofhate vertices fo the tetrahedron. Let a tetrahedron hve three of its vertices reresented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centrod lies at the point (2,3,5). THe coordinate of the fourth vertex of the tetrahedron is

A tetahedron is a three dimensional figure bounded by forunon coplanar trianglular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates (x_1,y_1,z_1)(x_2,y_2,zs_2),(x_3,y_3,z_3) and (x_4,y_4,z_4) respectivley in a rectngular three dimensionl space. Then the coordinates of tis centroid are (x_1+x_2+x_3+x4)/4, (y_1+y_2+y_3+4)/4, (z_1+z_2+z_3+z_4)/4 . the circumcentre of the tetrahedron is th centre of a sphere pssing thorugh its vetices. So, this is a point equidistasnt from each ofhate vertices fo the tetrahedron. Let a tetrahedron hve three of its vertices reresented by the points (0,0,0) ,(6,5,1) and (-4,1,3) and its centrod lies at the point (2,3,5). THe coordinate of the fourth vertex of the tetrahedron is

A tetrahedron is a three dimensional figure bounded by four non coplanar triangular plane.So a tetrahedron has four no coplnar points as its vertices. Suppose a tetrahedron has points A,B,C,D as its vertices which have coordinates (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) respectively in a rectangular three dimensional space. Then the coordinates of its centroid are ((x_1+x_2+x_3+x_3+x_4)/4, (y_1+y_2+y_3+y_3+y_4)/4, (z_1+z_2+z_3+z_3+z_4)/4) . the circumcentre of the tetrahedron is the center of a sphere passing through its vertices. So, this is a point equidistant from each of the vertices of the tetrahedron. Let a tetrahedron have three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,2,5). The coordinate of the fourth vertex of the tetrahedron is

A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (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)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The distance between the planes x + 2y- 3z -4 =0 and 2x + 4y - 6z=1 along the line x/1= (y)/(-3) = z/2 is :

A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (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)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The equation of the triangular plane of tetrahedron that contains the given vertices is :

A tetrahedron is three dimensional figure bounded by four non coplanar triangular plane. So a tetrahedron has points A,B,C,D as its vertices, which have coordinates (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)) respectively in a rectangular three –dimensional space. Then the coordinates of its centroid are ((x_(1)+ x_(2) + x _(3) + x_(4))/(4) , (y _(1) + y _(2) + y_(3) + y _(4))/(4), (z_(1) + z_(2) + z_(3)+ z_(4))/(4)). The circumcentre of the tetrahedron is the centre of a sphere passing through its vertices. So, the circumcentre is a point equidistant from each of the vertices of tetrahedron. Let tetrahedron has three of its vertices represented by the points (0,0,0) ,(6,-5,-1) and (-4,1,3) and its centroid lies at the point (1,-2,5). Now answer the following questions The coordinate of the fourth vertex of the tetrahedron is :

Find the coordinates 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) .

Show that the coordinates off the centroid of the triangle with vertices A(x_1, y_1, z_1),\ B(x_2, y_2, z_2)a n d\ (x_3, y_3, z_3) are ((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3,(z_1+z_2+z_3)/3)

Show that the centroid of the triangle with vertices A(x_1,\ y_1,\ z_1) , B(x_2,\ y_2,\ z_2) and A(x_3,\ y_3,\ z_3) has the coordinates (("x"_1+"x"_2+"x"_2)/3,("y"_1+"y"_2+"y"_2,)/3("z"_1+"z"_2+"z"_2)/3)

Show that the lines (x-4)/(1)=(y+3)/(-4)=(z+1)/7 and (x-1)/(2) =(y+1)/(-3)=(z+10)/(8) intersect. Find the coordinates of their point of intersection.