Q 39.

Question

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <\frac{1}{5}, \frac{1}{3}>$

Step-by-Step Solution

Verified

Answer

$||v|| = \frac{\sqrt{34}}{15}$ and the unit vector in the direction of v is $\frac{15}{\sqrt{34}} <\frac{1}{5}, \frac{1}{3}>$ .

1Step 1. Given information.

The given vector is:

$v = <\frac{1}{5}, \frac{1}{3}>$

2Step 2. Find the norm of the vector.

$v = <\frac{1}{5}, \frac{1}{3}> ||v|| = \sqrt{{(\frac{1}{5})}^{2} + {(\frac{1}{3})}^{2}} = \sqrt{\frac{1}{25} + \frac{1}{9}} = \sqrt{\frac{9 + 25}{225}} = \frac{\sqrt{34}}{15}$

Therefore, the norm of the given vector is $\frac{\sqrt{34}}{15}$ .

3Step 3. Find the unit vector in the direction of v .

The unit vector in the direction of v is the vector:

$\frac{1}{||v||} v = \frac{1}{\frac{\sqrt{34}}{15}} <\frac{1}{5}, \frac{1}{3}> = \frac{15}{\sqrt{34}} <\frac{1}{5}, \frac{1}{3}>$

Therefore, the unit vector in the direction of $v = <\frac{1}{5}, \frac{1}{3}>$ is $\frac{15}{\sqrt{34}} <\frac{1}{5}, \frac{1}{3}>$ .

Q 38.

Q 40.

Other exercises in this chapter

Q 37,

Find v and find the unit vector in the direction of v.v = 3, −4

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Q 38.

In Exercises 37–42, find v and find the unit vector in the direction of v.v=13,-23

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Q 40.

In Exercises 37–42, find v and find the unit vector in the direction of v.v=2,1,-5

View solution

Q 41.

In Exercises 37–42, find v and find the unit vector in the direction of v.v=1,1,1

View solution