Q8 of 230 Page 29

Find the equation of a plane which is at a distance of 3√3 units from the origin and the normal to which is equally inclined with the coordinate axes.

Let and be the angles made by with x, y and z - axes respectively.

It is given that


α = β = γ


cos α = cos β = cos γ


l = m = n, where l, m, n are direction cosines of.


But l2 + m2 + n2 = 1


Or, l2 + l2 + l2 = 1


Or, 3 l2 = 1


Or,


Or,


So, l = m = n =


It is given that the length of the perpendicular of the plane from the origin, p =


The normal form of the plane is lx + my + nz = p.





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