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

Question

asked Jun 25, 2023 9.2k views

1 Answer

Krys · Answer 1 · 2023-06-29T19:22:36+0000

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

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