Chapter 9: Q. 64 (page 622)

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

Short Answer

Expert verified

The given vector is

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

Step by step solution

Step 1. Given

Vector v as:

$v = j + k$

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,

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

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

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=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

Decision Maths

Calculus

Geometry

Pure Maths

Statistics

Theoretical and Mathematical Physics

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).
$v = j + k$