Find unit vector (u) with the same direction
To find a unit vector (u) with the same direction as a given vector, you need to divide the given vector by its magnitude
To find a unit vector (u) with the same direction as a given vector, you need to divide the given vector by its magnitude.
Let’s say we have a vector v = (a, b, c). To find the unit vector u with the same direction as v, we follow these steps:
1. Find the magnitude (length) of the vector v:
magnitude of v = sqrt(a^2 + b^2 + c^2)
2. Divide each component of v by its magnitude:
u = (a / magnitude of v, b / magnitude of v, c / magnitude of v)
3. Simplify u:
u = (a / sqrt(a^2 + b^2 + c^2), b / sqrt(a^2 + b^2 + c^2), c / sqrt(a^2 + b^2 + c^2))
Now, vector u is a unit vector with the same direction as vector v.
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