Question

Question 8 Find the unit vector in the direction of (2,-3). Write your answer in component form. Do not approximate any numbers in your answer.

Answer 1

The unit vector in component form is
`\hat{u} = \left((2)/(√(13) ),-(3)/(√(13)) \right)` or
`\hat{u} = (2)/(√(13))\,i-(3)/(13)\,j`.

Explanation:

Let be
`\vec u = (2,-3)`, its unit vector is determined by following expression:

`\hat {u} = (\vec u)/(\|\vec u \|)`

Where
`\|\vec u \|` is the norm of
`\vec u`, which is found by Pythagorean Theorem:

`\|\vec u\|=\sqrt{2^(2)+(-3)^(2)}`

`\|\vec u\| = √(13)`

Then, the unit vector is:

`\hat{u} = (1)/(√(13)) \cdot (2,-3)`

`\hat{u} = \left((2)/(√(13) ),-(3)/(√(13)) \right)`

The unit vector in component form is
`\hat{u} = \left((2)/(√(13) ),-(3)/(√(13)) \right)` or
`\hat{u} = (2)/(√(13))\,i-(3)/(13)\,j`.