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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 47 (page 622)

In Problems 45鈥�50, find the unit vector in the same direction as v.
$v = 3 i - 6 j - 2 k$

Short Answer

Expert verified

The unit vector in the same direction as $v = 3 i - 6 j - 2 k$ is $\frac{3}{7} i - \frac{6}{7} j - \frac{2}{7} k$

Step by step solution

01

Step 1. Given

The vector $v = 3 i - 6 j - 2 k$

To find the unit vector.

02

Step 2. Unit vector in the direction of v

For any nonzero vector v, the vector $u = \frac{v}{||v||}$ is a unit vector that has the same direction as v.

03

Step 3. Find v

Now,

$||v|| = ||3 i - 6 j - 2 k|| = \sqrt{3^{2} + {(- 6)}^{2} + {(- 2)}^{2}} = \sqrt{9 + 36 + 4} = \sqrt{49} = 7$

04

Step 4. Find the unit vector.

The unit vector is,

$u = \frac{v}{||v||} = \frac{3 i - 6 j - 2 k}{7} = \frac{3}{7} i - \frac{6}{7} j - \frac{2}{7} k$

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Most popular questions from this chapter

True or False The tests for symmetry in polar coordinates are necessary but not sufficient.

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

$r = 3^{胃}$

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(- 2, \frac{3 蟺}{4})$

find each quantity if $v = 3 i - 5 j$ and $w = - 2 i + 3 j$

$||v + w||$

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

$3 v + u - 2 w$

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