Chapter 9.4, Problem 52AYU

To determine

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

Answer to Problem 52AYU

Solution:

  $\frac{2\sqrt{5}}{5}i-\frac{\sqrt{5}}{5}j$

Explanation of Solution

Given:

  $v=2i-j$

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 $a_1=2;b_1=-1$ .

  $\Vert v\Vert =\sqrt{{(2)}^2+{(-1)}^2}=\sqrt{4+1}=\sqrt{5}$

Unit vector $u=\frac{v}{\Vert v\Vert }=\frac{2i-j}{\sqrt{5}}=\frac{2}{\sqrt{5}}i-\frac{1}{\sqrt{5}}j=\frac{2\sqrt{5}}{5}i-\frac{\sqrt{5}}{5}j$ .