Let PM be the perpendicular from the point P(1,2,3) to the x-y plane .lf OP→  makes an angle θ with the positive direction of the z-axis and OM→ makes an angle ϕ with the positive direction of x-axis, where O is the origin and θ and ϕ are acute angles, then

If P be (x, y, z), then from the figure, x=rsin⁡θcos⁡ϕ,y=rsin⁡θsin⁡ϕ and z=rcos⁡θ1=rsin⁡θcos⁡ϕ,2=rsin⁡θsin⁡ϕ and 3=rcos⁡θ⇒ 12+22+32=r2 or r=±14∴ sin⁡θcos⁡ϕ=114,sin⁡θsin⁡ϕ=214 and cos⁡θ=314(neglecting negative sign as θ and ϕ are acute) sin⁡θsin⁡ϕsin⁡θcos⁡ϕ=21Also,  tanθ=53