Find a unit vector that is orthogonal to both i + j and i + k

Vectors:

i = [1 0 0]

j = [0 1 0]

k = [0 0 1]

i + j = [1 1 0]

i + k = [1 0 1]

We want a vector which is orthogonal to both i + j and i + k, so the escalar procut between our vector "v" and i + j, i + k is equal to 0

Let's say v = [x y z]

v . (i + j) = [x y z] . [1 1 0] = x.1 + y.1 + z.0 = 0 => x + y = 0

v . (i + k) = [x y z] . [1 0 1] = x.1 + y.0 + z.1 = 0 => x + z = 0

So, we can say:

x + y = 0 => x = -y

x + z = 0 => x = -z

If x = -y:

x + z = 0

-y + z = 0

z = y = a and x = -a

We know it's a unit vector, so:

So,

y = z = a = and x = -a =

v = [ ]

answer: .64

step-by-step explanation

set up the formula for standard deviation for this set of numbers, then simplify