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Dot product in vector format = (1×0)i + (1×1)j + (0×1)k
= 1 j
By magnitude, it's 1.
Now we find the dot product using the magnitudes of the vectors.
The magnitude of each vector is (1+1)^½ = 2^½
Dot product of these vectors = 2^½ × 2^½ × cos theta
= 2 cos theta
We have already established before that the dot product of these vectors is 1
So...
2 cos theta = 1
cos theta = ½
theta = 60°