Question

Find the unit vector in the direction of (-4,5).Write your answer in component form.

Answer 1

The vector is given in the form d = (x, y)

The unit vector is given the formulae below:

`\hat{d}=(x)/(|d|)+(y)/(|d|)`

STEP 1

First we get the magnitude of the vector, |m|. This is gotten as:

`\begin{gathered} |d|\text{ = }\sqrt[]{x^2+y^2} \\ |d|\text{ = }\sqrt[]{(-4)^2+5^2}=\sqrt[]{16+25}=\sqrt[]{41} \end{gathered}`

STEP 2

We input the values into the formula to determine the unit vector

`\hat{d}=\frac{-4\hat{i}}{\sqrt[]{41}}+\frac{5\hat{j}}{\sqrt[]{41}}`