Chapter 9: Q. 41 (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 $\sqrt{105}$

Step by step solution

Step 1. Given

The quantities:

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

To find the given values.

Step 2. Combine like terms.

Combine like terms.

$||v - w|| = ||3 i - 5 j + 2 k - (- 2 i + 3 j - 2 k)|| = ||3 i - 5 j + 2 k + 2 i - 3 j + 2 k|| = ||5 i - 8 j + 4 k||$

Step 3. Find the length of the vector

The length of the factor is,

$||5 i - 8 j + 6 k|| = \sqrt{5^{2} + {(- 8)}^{2} + 4^{2}} = \sqrt{25 + 64 + 16} = \sqrt{105} = \sqrt{105}$

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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

Step by step solution

Step 1. Given

Step 2. Combine like terms.

Step 3. Find the length of the vector

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In Problems 39–44, find each quantity if v=3i-5j+2kandw=-2i+3j-2kv-w

Short Answer

Step by step solution

Step 1. Given

Step 2. Combine like terms.

Step 3. Find the length of the vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Decision Maths

Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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