Let t be a fixed number and let and and .
Show that is a unit vector.
Hint:
Not sure how that even helps unless I want to the hint via induction.
Sorry, but I don't quite understand your question.
I just wrote down what, imho, the square of the length of that vector happens do be: namely the sum of the squares of its coordinates. Hence I get
Can you be a bit more specific as to where, exactly the occurrence of in what I wrote surprises you?