Q. 53 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. 53 (page 627)

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

Short Answer

Expert verified

$\hat{a} = \frac{11 \hat{i} + \hat{j} + 7 \hat{k}}{\sqrt{171}}$

Step by step solution

Step 1. Given vectors in the plane

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

Step 2. The cross product

We know that the unit vector perpendicular to $\overset{鈫�}{v} & \overset{鈫�}{w}$

is :role="math" localid="1646870930687" $\hat{a} = 卤 \frac{\overset{鈫�}{v} 脳 \overset{鈫�}{w}}{|\overset{鈫�}{v} 脳 \overset{鈫�}{w}|}$

So;

$\overset{鈫�}{v} = \hat{i} + 3 \hat{j} - 2 \hat{k} \overset{鈫�}{w} = - 2 \hat{i} + \hat{j} + 3 \hat{k} \overset{鈫�}{v} 脳 \overset{鈫�}{w} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 3 & - 2 \\ - 2 & 1 & 3 \end{matrix}| \overset{鈫�}{v} 脳 \overset{鈫�}{w} = \hat{i} (9 + 2) - \hat{j} (3 - 4) + \hat{k} (1 + 6) \overset{鈫�}{v} 脳 \overset{鈫�}{w} = 11 \hat{i} + \hat{j} + 7 \hat{k} | \overset{鈫�}{v} 脳 \overset{鈫�}{w} | = \sqrt{121 + 1 + 49} | \overset{鈫�}{v} 脳 \overset{鈫�}{w} | = \sqrt{171}$

Step 3. The unit vector is :

$\hat{a} = \frac{11 \hat{i} + \hat{j} + 7 \hat{k}}{\sqrt{171}}$

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91影视

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

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�=i^+3j^-2k^w鈫�=-2i^+j^+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

Theoretical and Mathematical Physics

Decision Maths

Calculus

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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