 Hi friends, I am Poojwa and today we will discuss the following question and the following find the coordinates of the photo of the perpendicular drawn from the origin 3y plus 4z minus 6 is equal to 0 Let us begin with the solution now. Now we are given equation of the plane is 3y plus 4z minus 6 is equal to 0 or we can write this as 3y plus 4z is equal to 6 Let the coordinates of the foot of the perpendicular of point P from origin to the plane B x1, y1, z1 then the direction ratios of the line OPR x1, y1 and z1 Writing the equation of the plane in normal form we get 3y upon 5 plus 4z upon 5 is equal to 6 upon 5 Now this is the equation of the plane so writing this equation of the plane in normal form We get 3y upon 5 plus 4z upon 5 is equal to 6 upon 5 where we have This 5 is equal to under root of coefficient of x whole square that is 0 square plus coefficient of y whole square that is 3 square plus coefficient of z whole square that is 4 square Now this equation is of the form Lx plus my Plus NZ is equal to D which is the Cartesian equation of plane in normal form now Here we have L comma M comma N are the direction cosines of the normal and D is the distance of the plane from origin So comparing these two equations we can say here 0 comma 3 upon 5 comma 4 upon 5 are the direction cosines of the line OP now since the direction cosines and the direction ratios of a line are proportional We have x1 upon 0 is equal to y1 upon 3 upon 5 is equal to z1 upon 4 upon 5 is equal to some constant k here x1 y1 and z1 are the direction ratios and 0 3 upon 5 and 4 upon 5 are the direction cosines That is we have x1 is equal to 0 y1 is equal to 3k upon 5 and z1 is equal to 4k upon 5 Now substituting these values in the equation of the plane we get 3 into 3k upon 5 plus 4 into 4k upon 5 is equal to 6 This implies 9k plus 16k is equal to 30 which implies 25k is equal to 30 and this further implies k is equal to 6 upon 5 Now putting this value of k in one we get x1 is equal to 0 y1 is equal to 3 upon 5 into 6 upon 5 which is equal to 18 upon 25 and z1 is equal to 4 upon 5 into 6 upon 5 which is equal to 24 upon 25 thus the coordinates of the foot of the perpendicular are 0 comma 18 upon 25 comma 24 upon 25 So we have got our answer as 0 comma 18 upon 25 comma 24 upon 25. Hope you have understood the solution. Bye and take care