Three Dimensional Geometry Part 1

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 ‌

π

2