Chapter 9: Q. 59 (page 622)

In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 6 j - 2 k$

Short Answer

Expert verified

The given vector is

$v = 7 (\cos 64 . 6^{\circ} i + \cos 149 . 0^{\circ} j + \cos 106 . 6^{\circ} k)$

Step by step solution

Step 1. Given

Vector v as:

$v = 3 i - 6 j - 2 k$

Step 2. Concept

For a given vector in the xyz plane.

A directional angle is defined as :

$\cos α = \frac{a}{|v|} ∠ α a n g l e b e t w e e n v a n d x a x i s . \cos β = \frac{b}{|v|} ∠ β a n g l e b e t w e e n v a n d y a x i s . \cos γ = \frac{c}{|v|} ∠ γ a n g l e b e t w e e n v a n d z a x i s .$

Step 3. Calculation

Consider,

$v = 3 i - 6 j - 2 k l e t s f i n d t h e m a g n i t u d e o f v i . e . v = \sqrt{3^{2} + {(- 6)}^{2} + {(- 2)}^{2}} = \sqrt{49} = 7 N o w a p p l y a n g l e f o r m u l a t o g e t t h e r e s p e c t i v e a n g l e s \cos α = \frac{3}{7} α = \cos^{- 1} (\frac{3}{7}) \approx 64.6 β = \cos^{- 1} (\frac{- 6}{7}) \approx 149.0 γ = \cos^{- 1} (\frac{- 2}{7}) \approx 106.6 T h u s, v = 7 (\cos 64 . 6^{\circ} i + \cos 149 . 0^{\circ} j + \cos 106 . 6^{\circ} k)$

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In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 6 j - 2 k$

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

One App. One Place for Learning.

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In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).v=3i-6j-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

Decision Maths

Statistics

Pure Maths

Logic and Functions

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = 3 i - 6 j - 2 k$