Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find a unit vector in the direction opposite to $<3, 4, 5>$ .

The required vector is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given vector is:

$v = <3, 4, 5>$

Step 2. Find the norm of the vector.

$v = <3, 4, 5> ||v|| = \sqrt{3^{2} + 4^{2} + 5^{2}} = \sqrt{9 + 16 + 25} = \sqrt{50}$

Therefore, the norm of the given vector is $\sqrt{50}$ .

Step 3. Find the vector.

We know that the vector in the direction of v is $\frac{1}{||v||} (- v)$ . Here a is the magnitude of the given vector and the negative sign shows the direction opposite to $v = <3, 4, 5>$ .

The required vector is:

role="math" localid="1649521227299" $\frac{1}{||v||} v = \frac{1}{\sqrt{50}} (- <3, 4, 5>) = \frac{1}{\sqrt{50}} <- 3, - 4, - 5>$

Therefore, the unit vector in the direction opposite to $v = <3, 4, 5>$ is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

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Calculus

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Short Answer

Find a unit vector in the direction opposite to $<3, 4, 5>$ .

Step by Step Solution

Step 1. Given information.

Step 2. Find the norm of the vector.

Step 3. Find the vector.

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Calculus

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Short Answer

Find a unit vector in the direction opposite to 3,4,5.

Step by Step Solution

Step 1. Given information.

Step 2. Find the norm of the vector.

Step 3. Find the vector.

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Find a unit vector in the direction opposite to $<3, 4, 5>$ .