Q. 54 Find a unit vector normal to the... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 54 (page 603)

Find a unit vector normal to the plane containing
$\overset{鈫�}{v} = 2 \hat{i} + 3 \hat{j} - \hat{k} \overset{鈫�}{w} = - 2 \hat{i} - 4 \hat{j} + 3 \hat{k}$

Short Answer

Expert verified

$\hat{a} = \frac{- 13}{\sqrt{237}} \hat{i} + \frac{8}{\sqrt{237}} \hat{j} - \frac{2}{\sqrt{237}} \hat{k}$

Step by step solution

Step 1. Given vectors in the plane

$\overset{鈫�}{v} = 2 \hat{i} + 3 \hat{j} - \hat{k} \overset{鈫�}{w} = - 2 \hat{i} - 4 \hat{j} + 3 \hat{k}$

Step 2. The cross product

We know that the unit vector perpendicular to

is:

$\hat{a} = 卤 \frac{\overset{鈫�}{v} 脳 \overset{鈫�}{w}}{|\overset{鈫�}{v} 脳 \overset{鈫�}{w}|}$

So;

$\overset{鈫�}{v} = 2 \hat{i} + 3 \hat{j} - \hat{k} \overset{鈫�}{w} = - 2 \hat{i} - 4 \hat{j} - 3 \hat{k} \overset{鈫�}{v} 脳 \overset{鈫�}{w} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & - 1 \\ - 2 & - 4 & - 3 \end{matrix}| \overset{鈫�}{v} 脳 \overset{鈫�}{w} = \hat{i} (- 9 - 4) - \hat{j} (- 6 - 2) + \hat{k} (- 8 + 6) \overset{鈫�}{v} 脳 \overset{鈫�}{w} = - 13 \hat{i} + 8 \hat{j} - 2 \hat{k} | \overset{鈫�}{v} 脳 \overset{鈫�}{w} | = \sqrt{169 + 4 + 64} | \overset{鈫�}{v} 脳 \overset{鈫�}{w} | = \sqrt{237}$

Step 3. The unit vector is :

$\hat{a} = \frac{- 13}{\sqrt{237}} \hat{i} + \frac{8}{\sqrt{237}} \hat{j} - \frac{2}{\sqrt{237}} \hat{k}$

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91影视

Find a unit vector normal to the plane containing
$\overset{鈫�}{v} = 2 \hat{i} + 3 \hat{j} - \hat{k} \overset{鈫�}{w} = - 2 \hat{i} - 4 \hat{j} + 3 \hat{k}$

Short Answer

Step by step solution

Step 1. Given vectors in the plane

Step 2. The cross product

Step 3. The unit vector is :

One App. One Place for Learning.

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91影视

Find a unit vector normal to the plane containingv鈫�=2i^+3j^-k^w鈫�=-2i^-4j^+3k^

Short Answer

Step by step solution

Step 1. Given vectors in the plane

Step 2. The cross product

Step 3. The unit vector is :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

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Study anywhere. Anytime. Across all devices.

Find a unit vector normal to the plane containing
$\overset{鈫�}{v} = 2 \hat{i} + 3 \hat{j} - \hat{k} \overset{鈫�}{w} = - 2 \hat{i} - 4 \hat{j} + 3 \hat{k}$