/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 Express the vector from \(P(-1,-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 8

Express the vector from \(P(-1,-4,6)\) to \(Q(1,3,-6)\) as a position vector in terms of \(\mathbf{i}, \mathbf{j},\) and \(\mathbf{k}\)

Short Answer

Expert verified
Question: Given points P(-1, -4, 6) and Q(1, 3, -6) in 3D space, find the vector from point P to point Q in terms of i, j, and k components. Answer: The vector from point P to point Q is 2i + 7j - 12k.

Step by step solution

01

Identify the coordinates of points P and Q

Given: Point P has coordinates \((-1, -4, 6)\) Point Q has coordinates \((1, 3, -6)\)
02

Calculate the difference in coordinates

The difference between the coordinates of point Q and point P is: \(\Delta x = 1 - (-1) = 2\) \(\Delta y = 3 - (-4) = 7\) \(\Delta z = -6 - 6 = -12\)
03

Express the vector in terms of i, j, and k components

The vector from point P to point Q in terms of i, j, and k components is given by: \(\vec{PQ} = \Delta x \cdot \mathbf{i} +\Delta y \cdot \mathbf{j} +\Delta z \cdot \mathbf{k} = 2 \cdot \mathbf{i} + 7 \cdot \mathbf{j} - 12 \cdot \mathbf{k}\)

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Proof of Sum Rule By expressing \(\mathbf{u}\) and \(\mathbf{v}\) in terms of their components, prove that $$\frac{d}{d t}(\mathbf{u}(t)+\mathbf{v}(t))=\mathbf{u}^{\prime}(t)+\mathbf{v}^{\prime}(t)$$

A golfer launches a tee shot down a horizontal fairway; it follows a path given by \(\mathbf{r}(t)=\left\langle a t,(75-0.1 a) t,-5 t^{2}+80 t\right\rangle,\) where \(t \geq 0\) measures time in seconds and \(\mathbf{r}\) has units of feet. The \(y\) -axis points straight down the fairway and the \(z\) -axis points vertically upward. The parameter \(a\) is the slice factor that determines how much the shot deviates from a straight path down the fairway. a. With no slice \((a=0),\) sketch and describe the shot. How far does the ball travel horizontally (the distance between the point the ball leaves the ground and the point where it first strikes the ground)? b. With a slice \((a=0.2),\) sketch and describe the shot. How far does the ball travel horizontally? c. How far does the ball travel horizontally with \(a=2.5 ?\)

Proof of Cross Product Rule Prove that $$\frac{d}{d t}(\mathbf{u}(t) \times \mathbf{v}(t))=\mathbf{u}^{\prime}(t) \times \mathbf{v}(t)+\mathbf{u}(t) \times \mathbf{v}^{\prime}(t)$$ There are two ways to proceed: Either express \(\mathbf{u}\) and \(\mathbf{v}\) in terms of their three components or use the definition of the derivative.

Prove the following vector properties using components. Then make a sketch to illustrate the property geometrically. Suppose \(\mathbf{u}, \mathbf{v},\) and \(\mathbf{w}\) are vectors in the \(x y\) -plane and a and \(c\) are scalars. $$a(c \mathbf{v})=(a c) \mathbf{v}$$

Compute \(\mathbf{r}^{\prime \prime}(t)\) and \(\mathbf{r}^{\prime \prime \prime}(t)\) for the following functions. $$\mathbf{r}(t)=\tan t \mathbf{i}+\left(t+\frac{1}{t}\right) \mathbf{j}-\ln (t+1) \mathbf{k}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.