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Chapter 9: Q. 42 (page 621)

In Problems 39–44, find each quantity if $v = 3 i - 5 j + 2 k a n d w = - 2 i + 3 j - 2 k$
$||v + w||$

Short Answer

Expert verified

The value of $||v + w||$ is $\sqrt{5}$

Step by step solution

01

Step 1. Given

The quantities:

$v = 3 i - 5 j + 2 k; w = - 2 i + 3 j - 2 k$

To find the given values.

02

Step 2. Combine like terms

Combine like terms

$||v + w|| = ||3 i - 5 j + 2 k + (- 2 i + 3 j - 2 k)|| = ||i - 2 j||$

03

Step 3. Find the length of the vector

The length of the factor is,

$||i - 2 j|| = \sqrt{1^{2} + {(- 2)}^{2}} = \sqrt{1 + 4} = \sqrt{5}$

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Most popular questions from this chapter

find the unit vector in the same direction as $v$

$v = - 5 i + 12 j$

In Problems 61–66, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph.

$r = 3; r = 2 + 2 \cos θ$

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 1 - \cos θ$

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 2 + 2 \cos θ$

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 4 \cos (3 θ)$

See all solutions

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