`P^1(x^1,y^1,z^1)` Image of point `P.` How find `P^1`

Find the coordinates of the foot of the perpendicular and the perpendicular distance from the point P(3,2,1) to the plane 2x-y+z+1=0 Find also the image of the point P in the plane.

Prove that if P(x,y) be any point on the line segment joining P_(1)(x_(1),y_(1)) and P_(2) (x_(2),y_(2)) then x=x_(1)+k(x_(2)-x_(1)) and y=y_(1)+k(y_(2)-y_(1)) , where bar (P_(1)P), bar (P_(1)P_(2))=k What conclusion can you draw about the position of P if 0 lt k lt 1

Prove that if P(x,y) be any point on the line segment joining P_(1)(x_(1),y_(1)) and P_(2) (x_(2),y_(2)) then x=x_(1)+k(x_(2)-x_(1)) and y=y_(1)+k(y_(2)-y_(1)) , where bar (P_(1)P), bar (P_(1)P_(2))=k What conclusion can you draw about the position of P if k gt 1

Find the image of the point p wrt the plane L where P-=(1,2,3) and L=2x+2y+4z=38

If a,b,c are in G.P and a^(1/x)=b^(1/y)=c^(1/z) then prove that x,y,z are in A.P.

If x,y,z are in A.P. and tan^(-1)x, tan^(-1)y and tan^(-1)z are also in A.P. then