Chapter 9: Q. 51 (page 603)

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

Short Answer

Expert verified

The unit vector in the same direction as $v$ is $\frac{1}{\sqrt{2}} i - \frac{1}{\sqrt{2}} j$ .

Step by step solution

Step 1. Magnitude of the Vector

The given vector $v = i - j$

Th magnitude of the given vector is $\sqrt{1 + 1} = \sqrt{2}$

Step 2. Unit Vector in the direction of v

Now, we multiply the scaler $\frac{1}{|v|} = \frac{1}{\sqrt{2}}$ . A unit vector in the same direction as $v$ is:

$\frac{v}{‖ v ‖} = \frac{i - j}{\sqrt{2}} = \frac{1}{\sqrt{2}} i - \frac{1}{\sqrt{2}} j$

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

Short Answer

Step by step solution

Step 1. Magnitude of the Vector

Step 2. Unit Vector in the direction of v

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In Problems 47–52, find the unit vector in the same direction asv:v=i-jv=i-j

Short Answer

Step by step solution

Step 1. Magnitude of the Vector

Step 2. Unit Vector in the direction of v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

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