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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. 50 (page 622)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given

The vector $v = 2 i - j + k$

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,

$||v|| = ||2 i - j + k|| = \sqrt{2^{2} + {(- 1)}^{2} + 1^{2}} = \sqrt{4 + 1 + 1} = \sqrt{6}$

04

Step 4. Find the unit vector.

The unit vector is,

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

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Most popular questions from this chapter

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

$3 v + u - 2 w$

Write the expression in the standard form $a + i b$ .

${[5 (\cos \frac{3 蟺}{16} + i \sin \frac{3 蟺}{16})]}^{4}$

Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 1 - 2 \sin 胃$

Identify and graph each polar equation. Verify your graph using a graphing utility.
$r = 1 + 2 \sin 胃$

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

See all solutions

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