Chapter 9: Q. 63 (page 622)

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

Short Answer

Expert verified

The given vector is
$v = \sqrt{2} (\cos 45^{\circ} i + \cos 45^{\circ} j + \cos 90^{\circ} k)$

Step by step solution

Step 1. Given

Vector v as:

$v = i + j$

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,

$v = i + j l e t s f i n d t h e m a g n i t u d e o f v i . e . v = \sqrt{1^{2} + {(1)}^{2} + 0^{2}} = \sqrt{2} N o w a p p l y a n g l e f o r m u l a t o g e t t h e r e s p e c t i v e a n g l e s \cos α = \frac{1}{\sqrt{2}} α = \cos^{- 1} (\frac{1}{\sqrt{2}}) \approx 45 β = \cos^{- 1} (\frac{1}{\sqrt{2}}) \approx 45 γ = \cos^{- 1} (\frac{0}{\sqrt{2}}) \approx 90 T h u s, v = \sqrt{2} (\cos 45^{\circ} i + \cos 45^{\circ} j + \cos 90^{\circ} k)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

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

Geometry

Logic and Functions

Pure Maths

Probability and Statistics

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

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

Geometry

Logic and Functions

Pure Maths

Probability and Statistics

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).
$v = i + j$