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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. 53 (page 603)

Find a vector $v$ whose magnitude is $4$ and whose component
in the $i$ direction is twice the component in the $j$ direction.

Short Answer

Expert verified

The vector is $\frac{8}{\sqrt{5}} i + \frac{4}{\sqrt{5}} j$

Step by step solution

01

Step 1. Given information

According to the question the vector will be,

$v = 2 x i + x j$

02

Step 2. Magnitude of the vector

The magnitude of the vector $v = 2 x i + x j$ is $\sqrt{4 x^{2} + x^{2}} = 4$

$\sqrt{5 x^{2}} = 4 5 x^{2} = 16 x^{2} = \frac{16}{5} x = \frac{4}{\sqrt{5}}$

03

Step 3. Required vector

Now the vector will be

$v = 2 x i + x j v = 2 (\frac{4}{\sqrt{5}}) i + \frac{4}{\sqrt{5}} j v = \frac{8}{\sqrt{5}} i + \frac{4}{\sqrt{5}} j$

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