Consider vectors u1 1 1 0 0 u2 1 0 1 0 and u3 1 0 0 1 in

Consider vectors u1 = (1, 1, 0, 0), u2 = (1, 0, 1, 0) and u3 = (1, 0, 0, 1) in R 4 . If the angle between u = (r, s, 2, t), for r, s, t R, and each of u1, u2, u3 is equal /2 then r + s + t equals what?

Solution

Since vector are perpendicular dot product will be zero, hence

r+s=0

r+2=0

r+t=0

Now,

r+2 =0, hence r = -2

Next,

r+s=0, hence s= -r =2

Also,

r+t=0, hence t= -r = 2

Thus r+s+t= -2+2+2 =2

Answer is 2