Chapter 9: Q. 42 (page 630)

In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
$||v|| - ||w||$

Short Answer

Expert verified

The expression $||v|| - ||w|| = 0 .$

Step by step solution

Step 1. Given Information

The given vectors are $v = 3 i + j - 2 k a n d w = - 3 i + 2 j - k .$

Step 2. Finding the given expression

To find the expression, substitute the values of vectors in the given expression.

Thus, $||v|| - ||w|| = ||3 i + j - 2 k|| - ||- 3 i + 2 j - k||$

As we know the length of a vector can be found as

$||v|| = ||a i + b j + c k|| ||v|| = \sqrt{a^{2} + b^{2} + c^{2}}$

Step 3. Solve

By proceeding with the calculation further

$||v|| - ||w|| = ||3 i + j - 2 k|| - ||- 3 i + 2 j - k|| = \sqrt{3^{2} + 1^{2} + {(- 2)}^{2}} - \sqrt{{(- 3)}^{2} + 2^{2} + {(- 1)}^{2}} = \sqrt{14} - \sqrt{14} = 0$

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In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
$||v|| - ||w||$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the given expression

Step 3. Solve

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In Problems 40–45, use the vectors v=3i+j-2kand w=-3i+2j-kto find each expression. v-w

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the given expression

Step 3. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Discrete Mathematics

Statistics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 40–45, use the vectors $v = 3 i + j - 2 k$ and $w = - 3 i + 2 j - k$ to find each expression.
$||v|| - ||w||$