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)`.

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

The coordinates of the point which divides the line joining (x_(1),y_(1)) and (x_(2),y_(2))

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)) .

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.

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))

The angle between the lines (x-1)/(2)=(y-2)/(1)=(z+3)/(2) and (x)/(1)=(y)/(1)=(z)/(0) is

If M(alpha , beta , gamma ) is the mid point of the line segment joining the points A(x_(1),y_(1),z_(1)) and B then find B.

Find the length of projection of the line segment joining the points (1,0,-1) and (-1,2,2) on the plane x+3y-5z=6 .

The point whose coordinates are x=x_(1)+t(x_(2)-x_(1)), y=y_(1)+t(y_(2)-y_(1)) divides the join of (x, y) and (x_(2), y_(2)) in the ratio