Final answer:
To find a unit vector that has the same direction as a given vector, divide the vector by its magnitude.
Step-by-step explanation:
To find a unit vector that has the same direction as a given vector, you need to divide the given vector by its magnitude. To find a unit vector that has the same direction as a given vector, divide the vector by its magnitude. The magnitude of a vector is found by taking the square root of the sum of the squares of its components.
For example, let's take the vector 2i + 2j + 2k. The magnitude of this vector is sqrt((2^2) + (2^2) + (2^2)) = 2 * sqrt(3). To find the unit vector in the same direction, divide each component of the vector by its magnitude: (2/(2 * sqrt(3)))i + (2/(2 * sqrt(3)))j + (2/(2 * sqrt(3)))k. Simplifying this expression gives sqrt(3)/3i + sqrt(3)/3j + sqrt(3)/3k.