Chapter 9: Q. 43 (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 $\sqrt{38} - \sqrt{17}$

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. Find the length of the vector.

Find the length of the vector separately.

$||v|| = ||3 i - 5 j + 2 k|| = \sqrt{3^{2} + {(- 5)}^{2} + {(2)}^{2}} = \sqrt{9 + 25 + 4} = \sqrt{38}$

$||w|| = ||- 2 i + 3 j - 2 k|| = \sqrt{{(- 2)}^{2} + 3^{2} + {(- 2)}^{2}} = \sqrt{17}$

Step 3. Find the required quantity.

The required value is,

$||v|| - ||w|| = \sqrt{38} - \sqrt{17}$

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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. Find the length of the vector.

Step 3. Find the required quantity.

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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. Find the length of the vector.

Step 3. Find the required quantity.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

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