Yes, it's from "The Cage" but it wasn't in the orignial Star Trek.
"The Cage" was the first pilot that was rejected by NBC. But the premise was the same. Strong, good looking captain. Older, wise doctor. A Vulcan science officer.
The big difference between this and the actual series was the merger of the "number two" position and the Spock character. He became both the science officer and the first officer instead of being two characters. Of course, Majel Barrett played number two in "The Cage" and became nurse Chapel.
Yes, I could have explained all that, but I was under a tight deadline. ; ' )