Final answer:
The values of m for which m(i + j + k) is a unit vector are m = 1/sqrt(3) and m = -1/sqrt(3).
Step-by-step explanation:
To find the values of m for which m(i + j + k) is a unit vector, we need to ensure that the magnitude of the vector is equal to 1.
The magnitude of the vector m(i + j + k) is given by: |m(i + j + k)| = sqrt((m^2 + m^2 + m^2)) = sqrt(3m^2).
So, in order for the vector to be a unit vector, we must have sqrt(3m^2) = 1.
Solving for m, we get m = +- 1/sqrt(3), which means that the values of m for which m(i + j + k) is a unit vector are m = 1/sqrt(3) and m = -1/sqrt(3).