If find the unit vector in the direction of

We need to find the unit vector in the direction of .

First, let us calculate .

As we have,

…(a)

…(b)

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.

…(c)

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.

Here, .

Thus, unit vector in the direction of is .