Question

Let u = <4, 3>. Find the unit vector in the direction of u, and write your answer in component form.


help me please

Answer 1

Answer on Question #42422 – Math – Analytic Geometry

1. Let $u = <4, 3>$. Find the unit vector in the direction of $u$, and write your answer in component form.

Solution.

The module of the vector $\vec{u}(4;3)$ is $|\vec{u}| = \sqrt{4^2 + 3^2} = 5$.

The unit vector in the direction of $u$ is $\vec{n} = \begin{vmatrix} \vec{u} \\ \vec{u} \end{vmatrix}$. The module of this vector equals to 1, and the direction is the same as the direction of the vector $\vec{u}$.

Let write the unit vector in component form: $\vec{n} = \frac{1}{5}(4;3) = \begin{pmatrix} 4 & 3 \\ 5 & 5 \end{pmatrix}$.

Answer: $\begin{pmatrix} 4 & 3 \\ 5 & 5 \end{pmatrix}$.