The vector is given in the form d = (x, y)
The unit vector is given the formulae below:
[tex]\hat{d}=\frac{x}{|d|}+\frac{y}{|d|}[/tex]STEP 1
First we get the magnitude of the vector, |m|. This is gotten as:
[tex]\begin{gathered} |d|\text{ = }\sqrt[]{x^2+y^2} \\ |d|\text{ = }\sqrt[]{(-4)^2+5^2}=\sqrt[]{16+25}=\sqrt[]{41} \end{gathered}[/tex]STEP 2
We input the values into the formula to determine the unit vector
[tex]\hat{d}=\frac{-4\hat{i}}{\sqrt[]{41}}+\frac{5\hat{j}}{\sqrt[]{41}}[/tex]