Solve velocity addition problems using 4-vector

Natchanon

Homework Statement
An inertial frame F' moves in the x direction with speed v = 0.9c relative to another frame F. A traveler is moving with velocity u' = 0.5c i + 0.5c j in the frame F'. Determine the traveler's velocity in the frame F.
Homework Equations
u_parallel = (u_parallel' + v)/(1+vu_parallel'/c^2)
u_perpen = u_perpen'/gamma(1+vu_perpen'/c^2)
I used the two equations above to solve for u_x and u_y and got u = 0.987c, where u_parallel = u_x and u_perpen = u_y. I wonder if I can use velocity four-vectors to solve this problem. Modify η = Λμνην so we can use it for velocity addition?

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