Chapter 9.4, Problem 47AYU

To determine

To find: Unit vector in the same direction as $v$.

Answer to Problem 47AYU

Solution:

$i$

Explanation of Solution

Given:

$v=5i$

Calculation:

Let $v=a_{1}i+b_{1}j=\langle a_1,b_1\rangle$. Then $\Vert v\Vert =\sqrt{a_1^2+b_1^2}$.

Here $a_1=5;b_1=0$.

$\Vert v\Vert =\sqrt{{\left(5\right)}^2+{\left(0\right)}^2}=\sqrt{25+0}=\sqrt{25}=5$

Unit vector $u=\frac{v}{\Vert v\Vert }=\frac{5i}{5}=i$.