Let the angle of line makes with the positive direction of z-axis is α direction cosines of line with the +ve directions of x-axis, y-axis, and z-axis is l,m,n respectively. ∴l=cos
π
4
,m=cos
π
4
,n=cosα as we know that, l2+m2+n2=1 ∴cos2
π
4
+cos2
π
4
+cos2α=1 ⇒
1
2
+
1
2
+cos2α=1 ⇒cos2α=0⇒α=
π
2
Hence, angle with positive direction of the z-axis is