Question

Find the unit vector in the direction of (-4,5).Write your answer in component form.Do not approximate any numbers in your answer.

Answer 1

We begin by calculating the magnitude of the given vevtor

`|\vec{v}|=\sqrt[]{v^2_1+v^2_2}`

where v₁ and v₂ are the components of the vector. In this case:

`|(-4,5)|=\sqrt[]{(-4)^2+5^2}=\sqrt[]{16+25}=\sqrt[]{41}`

Now, in order to find the unit vector in the direction of a given vector, we calculate

`\frac{\vec{v}}\vecv`

so in this case we have

`\frac{(-4,5)}{\sqrt[]{41}}=(\frac{-4}{\sqrt[]{41}},\frac{5}{\sqrt[]{41}})`