Question

Find four perpendicular unit vectors with all components equal to 1/2 or -1/2.

Answer 1

@Euler271

Answer 2

**make this happen that the sum of the 3 components equals zero.

Answer 3

So how does the answers look like?

Answer 4

since you need 4 unit vectors, so I suggest take the first one as standard in 4 dimensions, and its length is 1. Let say \(\vec a =(\dfrac{1}{2},\dfrac{1}{2},\dfrac{1}{2}, \dfrac{1}{2})\)
it satisfies your condition, right? all component is 1/2, unit vector ( since ||a|| =1 )
Please, be back to your previous question when you asked about the perpendicular vectors and I guided you how to find them. Do EXACTLY SAME. You will have what you need.
This time, the question is exactly the same the previous one, just change the condition that you have to find out the standard vector by yourself when it was given (1,1,1,1) in previous one. Now, I give you it. Yours responsibility is find them out by imitating the steps in previous case.
Good luck, girl.