Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 74

Find the vector \(\vec{C}\) that satisfies the equation \(3 \hat{x}+6 \hat{y}\) \(10 \hat{z}+\vec{C}=-7 \hat{x}+14 \hat{y}\)

Short Answer

Expert verified
Answer: The vector \(\vec{C}\) that satisfies the given equation is \(\vec{C} = -10 \hat{x} + 8 \hat{y} - 10 \hat{z}\).

Step by step solution

01

Write the given equation with vectors in component form

The equation provided is: \(3 \hat{x} + 6 \hat{y} + 10 \hat{z} + \vec{C} = -7 \hat{x} + 14 \hat{y}\) We can rewrite this equation in component form as follows: \((3, 6, 10) + \vec{C} = (-7, 14, 0)\)
02

Isolate vector \(\vec{C}\)

In order to determine vector \(\vec{C}\), we need to isolate it in the equation. We will subtract the vector \((3, 6, 10)\) from both sides of the equation: \(\vec{C} = (-7, 14, 0) - (3, 6, 10)\)
03

Subtract the vectors

Now, subtract the corresponding components in the two vectors on the right-hand side of the equation: \(\vec{C} = (-7-3, 14-6, 0-10)\)
04

Simplify the result

Finally, simplify the numerical operations in the components: \(\vec{C} = (-10, 8, -10)\) So, the vector \(\vec{C}\) that satisfies the given equation is \(\vec{C} = -10 \hat{x} + 8 \hat{y} - 10 \hat{z}\).

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Is mass a vector quantity? Why or why not?

Since the British system of units is more familiar to most people in the United States, why is the international (SI) system of units used for scientific work in the United States?

Find the magnitude and direction of (a) \(9 \vec{B}-3 \vec{A}\) and (b) \(-5 \vec{A}+8 \vec{B},\) where \(\vec{A}=(23.0,59.0), \vec{B}=(90.0,-150.0)\)

What metric prefixes correspond to the following powers of \(10 ?\) a) \(10^{3}\) b) \(10^{-2}\) c) \(10^{-3}\)

Given the equation \(w=x y z,\) and \(x=1.1 \cdot 10^{3}\), \(y=2.48 \cdot 10^{-2},\) and \(z=6.000,\) what is \(w,\) in scientific notation and with the correct number of significant figures?
See all solutions

Recommended explanations on Physics Textbooks

Medical Physics

Read Explanation

Electrostatics

Read Explanation

Rotational Dynamics

Read Explanation

Classical Mechanics

Read Explanation

Solid State Physics

Read Explanation

Radiation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free