Q. 65 In Problems 59 鈥� 66, find 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. 65 (page 622)

In Problems 59 鈥� 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 5 j + 2 k$

Short Answer

Expert verified

The given vector is

$v = \sqrt{38} (\cos 60 . 9^{鈭�} i + \cos 144 . 2^{鈭�} j + \cos 71 . 1^{鈭�} k)$

Step by step solution

Step 1. Given

Vector v as:

$v = 3 i - 5 j + 2 k$

Step 2. Concept

For a given vector in the xyz plane.

A directional angle is defined as :

$\cos 伪 = \frac{a}{|v|} 鈭� 伪 a n g l e b e t w e e n v a n d x a x i s . \cos 尾 = \frac{b}{|v|} 鈭� 尾 a n g l e b e t w e e n v a n d y a x i s . \cos 纬 = \frac{c}{|v|} 鈭� 纬 a n g l e b e t w e e n v a n d z a x i s .$

Step 3. Calculation

Consider,
$v = 3 i - 5 j + 2 k l e t s f i n d t h e m a g n i t u d e o f v i . e . v = \sqrt{3^{2} + {(- 5)}^{2} + {(2)}^{2}} = \sqrt{38} N o w a p p l y a n g l e f o r m u l a t o g e t t h e r e s p e c t i v e a n g l e s \cos 伪 = \frac{3}{\sqrt{38}} 伪 = \cos^{- 1} (\frac{3}{\sqrt{38}}) 鈮� 60.9 尾 = \cos^{- 1} (\frac{- 5}{\sqrt{38}}) 鈮� 144.2 纬 = \cos^{- 1} (\frac{2}{\sqrt{38}}) 鈮� 71.1 T h u s, v = \sqrt{38} (\cos 60 . 9^{鈭�} i + \cos 144 . 2^{鈭�} j + \cos 71 . 1^{鈭�} k)$

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91影视

In Problems 59 鈥� 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 5 j + 2 k$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

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91影视

In Problems 59 鈥� 66, find the direction angles of each vector. Write each vector in the form of equation (7).v=3i-5j+2k

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Calculus

Geometry

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 59 鈥� 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 5 j + 2 k$