The correct option is D 90∘
We know that cos of the angles made by a line segment with the positive direction of axes give us the direction cosines. Let the angle made with Z - axis be γ , where 0 ≤γ≤π
So, the direction cosines of OP will be cos30∘ ,cos60∘,cosγ
We know one property of direction cosines.
if the direction cosines of a line are l, m and n then
l2+m2+n2=1
So,(cos30∘)2+(cos60∘)2+(cosγ)2=1
Or,(√32)2+(cosγ)2=1
Or,(cosγ)2=0
Or cosγ=0
Since 0≤γ≤π the only possible value γ can have is π2 radians.
So, γ=90∘