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Q. 51

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Precalculus Enhanced with Graphing Utilities

Found in: Page 603

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 47–52, find the unit vector in the same direction as $v$ : $v = i - j$ $v = i - j$

The unit vector in the same direction as $v$ is $\frac{1}{\sqrt{2}} i - \frac{1}{\sqrt{2}} j$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Magnitude of the Vector

The given vector $v = i - j$

Th magnitude of the given vector is $\sqrt{1 + 1} = \sqrt{2}$

Step 2. Unit Vector in the direction of v

Now, we multiply the scaler $\frac{1}{|v|} = \frac{1}{\sqrt{2}}$ . A unit vector in the same direction as $v$ is:

$\frac{v}{‖ v ‖} = \frac{i - j}{\sqrt{2}} = \frac{1}{\sqrt{2}} i - \frac{1}{\sqrt{2}} j$

Most popular questions for Math Textbooks

In Problems 13–28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$θ = - \frac{π}{4}$

If $P = (- 3, 1) a n d Q = (x, 4)$ , find all numbers x such that the vector represented by $\overset{⇀}{P Q}$ has length 5.

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r^{2} = 9 \cos (2 θ)$

Use the vectors in the figure at the right to graph each of the following vectors.

$u - v$

Match the graph with the polar equation

$r \sin θ = 2$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 47–52, find the unit vector in the same direction as $v$ : $v = i - j$ $v = i - j$

Step by Step Solution

Step 1. Magnitude of the Vector

Step 2. Unit Vector in the direction of v

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 47–52, find the unit vector in the same direction as v:v=i-jv=i-j

Step by Step Solution

Step 1. Magnitude of the Vector

Step 2. Unit Vector in the direction of v

Most popular questions for Math Textbooks

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In Problems 47–52, find the unit vector in the same direction as $v$ : $v = i - j$ $v = i - j$