The coordinates of the foot of perpendicular drawn from origin to the plane 2 x - y + 5 z - 3 = 0 are ________

Step-by-step solution

Use foot of perpendicula ((x, y, z) ) of a point ( (x₁, y₁, z₁ ) ) in a plane (a x+b y+c z ) (+d=0 ) is given by ( x-x₁ a = y - y ₁ ~b = z - z ₁ c = -( ax ) Given equation of plane is (2 x-y+5 z-3 ) (=0 ) ( ) Foot of perpendicular drawn from origin to the given plane ( aligned & x-0 2 = y-0 -1 = z-0 5 &= -(0+0+0-3) (2)²+(-1)²+(5)² & x 2 = y -1 = z 5 = 3 30 = 1 10 & x 2 = 1 10 , y -1 = 1 10 , z 5 = 1 10 & x= 1 5 , y=- 1 10 , z= 1 2 aligned )