Given is the vector .

Let this vector be , such that

Let us first find the unit vector in the direction of this vector .

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.

Unit vector in the direction of the vector is given as,

As, we have .

Then,

[∵ if

]

Therefore,

[∵ and ]

We have found unit vector in the direction of the vector , but we need to find the unit vector in the direction of but also with the magnitude 9.

We have the formula:

Vector in the direction ofwith a magnitude of 9

And as just found.

So,

⇒Vector in the direction ofwith a magnitude of 9=

Thus, vector in the direction of vector and has magnitude 9 is .