 Hi friends, I am Pooja and today we will discuss the following question and the following find the coordinates of the foot of the perpendicular drawn from the origin. 5y plus 8 is equal to 0. Let us begin with the solution now. Now we are given equation of the plane is 5y plus 8 is equal to 0 or we can write this as 5y is equal to minus 8. 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, z1. Writing this equation of the plane in normal form we get y is equal to minus 8 upon 5. Now by dividing this equation by 5 we get y is equal to minus 8 upon 5 where this 5 is equal to under root of coefficient of x square that is 0 square plus coefficient of y square that is 5 square plus coefficient of z square that is 0 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 is equal to 0 and n is equal to 0 and m is equal to 1 where lm and n are the direction cosines of the normal and d is the distance of plane from the origin. So comparing these two equations we get here 0, 1, 0 are the direction cosines of the line OP. Now since the direction cosines and the direction ratios of a line are proportional we get now here x1, y1 and z1 are the direction ratios and 0, 1, 0 are the direction cosines and they both are proportional so we get x1 upon 0 is equal to y1 upon 1 is equal to z1 upon 0 is equal to some constant k that is we get x1 is equal to 0, y1 is equal to k and z1 is equal to 0 we mark this as 1. Now substituting these values in the equation of the plane we get 0 plus 5k plus 0 is equal to minus 8. Now this implies k is equal to minus 8 upon 5. Now putting this value of k in 1 we get x1 is equal to 0, y1 is equal to k that is minus 8 upon 5 and z1 is equal to 0 thus the coordinates of the foot of the perpendicular are 0 comma minus 8 upon 5 comma 0. So we have got our answer as 0 comma minus 8 upon 5 comma 0. Hope you have understood the solution. Bye and take care.