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)) .

Assertion (A): A(x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) . The projection of AB on the line with D.C's (l,m,n) is l(x_(2)-x_(1)) +m(y_(2)-y_(1))+n(z_(2)-z_(1)) Reason (R ) : The projection of the join of A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) on yz plane is sqrt((y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2))

A (x_(1),y_(1),z_(1)), B(x_(2),y_(2),z_(2)) are two points. Then the lenghts of projection on

Planes are drawn parallel to the coordinate planes through the points P (x_(1),y_(1),z_(1)) and Q (x_(2),y_(2),z_(2)) find the length of the edges of the parallopiped.

If the image of the point (-1, 3, 4) in the pane x - 2y =0 is (x _(1) , y _(1) , z _(1)) then z_(1) =

If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)=(x_(3)-2)^(2)+(y_(3)-3)^(2) then x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=

If (x_(1), y_(1), z_(1)), (x_(2), y_(2), z_(2)) and (x_(3), y_3), z_(3)) are the vertices of an equilateral triangle such that (x_(1)-2)^(2)+(y_(1)-3)^(2)+(z_(1)-4)^(2)=(x_(2)-2)^(2)+(y_(2)-3)^(2)+(z_(2)-4)^(2)=(x_(3)-2)^(3)+(y_(3)-3)^(2)+(z_(3)-4)^(2) then sum x_(1)+2sumy_(1)+3sum z_(1)=

Find the equation of the image of the plane x-2y+2z-3=0 in the plane x+y+z=1 .

Prove that the line segment joining (x_(1),y_(1),z_(1)) and (x_(2),y_(2),z_(2)) is divided by XY,YZ,ZX-plalnes respectively in the ratio -z_(1) : z_(2),-x_(1) :x_(2),-y_(1) : y_(2) .