How can I constraint camera on x axis only(character jumps but not camera), like any other sidescroller games
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All you have to do is to not change the other axis. Only update the X axis by breaking the position of the player, taking the x value and slot that into the X value of a new vector. Then that new resulting vector is the position of the camera.
If your camera is not on the XY plane you have to get the location of the camera and feed the YZ values into the new vector as well.