Final answer:
To find a unit vector with the same direction as the given vector, we divide the vector by its magnitude.
Step-by-step explanation:
To find a unit vector with the same direction as the given vector –7i+3j-k, we need to divide the vector by its magnitude. The magnitude of the given vector is sqrt((-7)^2 + 3^2 + (-1)^2) = sqrt(49 + 9 + 1) = sqrt(59).
So, to find the unit vector, we divide each component by the magnitude:
–7i/sqrt(59) + 3j/sqrt(59) - k/sqrt(59)
Therefore, the unit vector with the same direction as the given vector is approximately –0.919i + 0.397j − 0.083k.