Chapter 9.4, Problem 51AYU

To determine

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

Answer to Problem 51AYU

Solution:

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

Explanation of Solution

Given:

  $v=i-j$

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 $a_1=1;b_1=-1$ .

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

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