If the general equation of plane is given by ax + by + cz = d then a,b,c are the direction ratios of the normal to the plane.
If the general equation of plane is given by ax + by + cz = d then a,b,c are the direction ratios of the normal to the plane.
The correct option is A True
We know the normal equation of a plane is lx +my + nz = D , in which l, m,n are the direction cosines of the normal to the plane. We can clearly see that the difference between the normal form and the general form is that, in the normal form we have coefficient of x , y & z as the direction cosines and in the general form they are direction ratios. If we convert these ratios in the cosines we’ll get the normal form.
So, in the general equation of a plane “ D” is just a constant. in order make it the distance of the plane from origin we need to convert the direction ratios to direction cosines. If we do this we'll get the normal form.
So direction cosines from normal equation might remain as direction cosines or might become direction ratios. As direction cosines are also direction ratios we can say it is always direction ratios.
True
We know the normal equation of a plane is lx +my + nz = D , in which l, m,n are the direction cosines of the normal to the plane. We can clearly see that the difference between the normal form and the general form is that, in the normal form we have coefficient of x , y & z as the direction cosines and in the general form they are direction ratios. If we convert these ratios in the cosines we’ll get the normal form.
So, in the general equation of a plane “ D” is just a constant. in order make it the distance of the plane from origin we need to convert the direction ratios to direction cosines. If we do this we'll get the normal form.
So direction cosines from normal equation might remain as direction cosines or might become direction ratios. As direction cosines are also direction ratios we can say it is always direction ratios.
