We need to find the unit vector in the direction of .
First, let us calculate .
As we have,
Then multiply equation (a) by 2 on both sides,
We can easily multiply vector by a scalar by multiplying similar components, that is, vector’s magnitude by the scalar’s magnitude.
Subtract (b) from (c). We get,
We know that, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector.
For finding unit vector, we have the formula:
Now we know the value of , so we just need to substitute in the above equation.
Thus, unit vector in the direction of is .
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