Chapter 9: Q. 62 (page 622)

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

Short Answer

Expert verified

The given vector is

$v = \sqrt{3} (\cos 54 . 7^{\circ} i + \cos 125 . 3^{\circ} j + \cos 125 . 3^{\circ} k)$

Step by step solution

Step 1. Given

Vector v as:

$v = i - j - k$

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,

$v = i - j - k l e t s f i n d t h e m a g n i t u d e o f v i . e . v = \sqrt{1^{2} + {(- 1)}^{2} + {(- 1)}^{2}} = \sqrt{3} N o w a p p l y a n g l e f o r m u l a t o g e t t h e r e s p e c t i v e a n g l e s \cos α = \frac{1}{\sqrt{3}} α = \cos^{- 1} (\frac{1}{\sqrt{3}}) \approx 54.7 β = \cos^{- 1} (\frac{- 1}{\sqrt{3}}) \approx 125.3 γ = \cos^{- 1} (\frac{- 1}{\sqrt{3}}) \approx 125.3 T h u s, v = 7 (\cos 64 . 6^{\circ} i + \cos 149 . 0^{\circ} j + \cos 106 . 6^{\circ} k)$

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

Short Answer

Step by step solution

Step 1. Given

Step 2. Concept

Step 3. Calculation

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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=i-j-k

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

Geometry

Mechanics Maths

Probability and Statistics

Applied Mathematics

Pure Maths

Calculus

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).
$v = i - j - k$