Chapter 10: Q 37, (page 801)

Find $||v||$ and find the unit vector in the direction of $v$ .
$v = (3, - 4)$

Short Answer

Expert verified

The norm of the vector $v = (3, - 4)$ is $5$ and the unit vector in the direction of $v = (3, - 4)$ is $\frac{1}{5} (3, - 4)$ .

Step by step solution

Step 1. Given information .

We have given vector $v = (3, - 4)$ .

Step 2. Find the norm of the vector and unit vector in the direction of v.

$||v|| = \sqrt{a^{2} + b^{2}} = \sqrt{3^{2} + {(- 4)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

The unit vector in the direction of $v$ is $\frac{1}{||v||} v$ .

$\frac{1}{||v||} v = \frac{1}{5} (3, - 4)$

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Find $||v||$ and find the unit vector in the direction of $v$ .
$v = (3, - 4)$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the norm of the vector and unit vector in the direction of v.

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

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Find the norm of the vector and unit vector in the direction of v.

One App. One Place for Learning.

Most popular questions from this chapter

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Logic and Functions

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Study anywhere. Anytime. Across all devices.

Find $||v||$ and find the unit vector in the direction of $v$ .
$v = (3, - 4)$