Chapter 9: Q. 60 (page 622)

In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = - 6 i + 12 j + 4 k$

Short Answer

Expert verified

The given vector is

$v = 7 (\cos 115 . 4^{\circ} i + \cos 31 . 0^{\circ} j + \cos 73 . 4^{\circ} k)$

Step by step solution

Step 1. Given

Vector v as:

$v = - 6 i + 12 j + 4 k$

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,

$v = - 6 i + 12 j + 4 k l e t s f i n d t h e m a g n i t u d e o f v i . e . v = \sqrt{{(- 6)}^{2} + {(12)}^{2} + {(4)}^{2}} = \sqrt{196} = 14 N o w a p p l y a n g l e f o r m u l a t o g e t t h e r e s p e c t i v e a n g l e s \cos α = \frac{- 6}{14} α = \cos^{- 1} (- \frac{3}{7}) \approx 115.4 β = \cos^{- 1} (\frac{12}{14}) \approx 31.0 γ = \cos^{- 1} (\frac{4}{14}) \approx 73.4 T h u s, v = 7 (\cos 115 . 4^{\circ} i + \cos 31 . 0^{\circ} j + \cos 73 . 4^{\circ} k)$

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In Problems 59 – 66, find the direction angles of each vector. Write each vector in the form of equation (7).
$v = - 6 i + 12 j + 4 k$

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=-6i+12j+4k

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

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

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).
$v = - 6 i + 12 j + 4 k$