Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find a vector in the direction opposite to $<- 4, 5, - 1>$ and with magnitude 3.

The required vector is $\frac{3}{\sqrt{42}} <- 4, 5, - 1>$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given vector is:

$v = <- 4, 5, - 1>$ with magnitude 3.

Step 2. Find the norm of the vector.

$v = <- 4, 5, - 1> ||v|| = \sqrt{{(- 4)}^{2} + 5^{2} + {(- 1)}^{2}} = \sqrt{16 + 25 + 1} = \sqrt{42}$

Therefore, the norm of the given vector is $\sqrt{42}$ .

Step 3. Find the vector.

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

The required vector is:

$\frac{a}{||v||} v = \frac{3}{\sqrt{42}} (- <- 4, 5, - 1>) = \frac{3}{\sqrt{42}} <4, - 5, 1>$

Therefore the vector in the direction opposite to $v = <- 4, 5, - 1>$ and with a magnitude of is $\frac{3}{\sqrt{42}} <4, - 5, 1>$ .

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Calculus

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Short Answer

Find a vector in the direction opposite to $<- 4, 5, - 1>$ and with magnitude 3.

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 vector in the direction opposite to -4,5,-1 and with magnitude 3.

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 vector in the direction opposite to $<- 4, 5, - 1>$ and with magnitude 3.