Chapter 9: Q. 59 (page 603)

Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 14 α = 120^{o}$

Short Answer

Expert verified

The vector v can be written as $- 7 i + 7 \sqrt{3} j$ .

Step by step solution

Step 1. Given information

We have been given:
$||v|| = 14 α = 120^{o}$

We have to write it in ai+bj form.

Step 2. Substitute the values in v=v(cosαi+sinαj).

$\begin{aligned} v = 14 (\cos (120^{\circ}) i + \sin (120^{\circ}) j) \\ v = 14 \cdot (- \frac{1}{2} i + \frac{\sqrt{3}}{2} j) \\ v = - \frac{14}{2} i + \frac{14 \sqrt{3}}{2} j \\ v = - 7 i + 7 \sqrt{3} j \end{aligned}$

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.

Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 14 α = 120^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute the values in v=v(cosαi+sinαj).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write the vector v in the form ai + bj, given its magnitude vand the angle αit makes with the positive x-axis.v=14α=120o

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute the values in v=v(cosαi+sinαj).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 14 α = 120^{o}$