Chapter 9: Q. 41 (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 $||v - w|| = \sqrt{38} .$

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,

$||v - w|| = ||(3 i + j - 2 k) - (- 3 i + 2 j - k)|| = ||6 i - j - k||$

As we know the length of a vector can be found as $||v|| = ||a i + b j + c k|| ||v|| = \sqrt{a^{2} + b^{2} + c^{2}}$

So,

$||v - w|| = ||6 i - j - k|| ||v - w|| = \sqrt{6^{2} + {(- 1)}^{2} + {(- 1)}^{2}} ||v - w|| = \sqrt{38}$

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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

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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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Pure Maths

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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.
$||v - w||$