Chapter 9: Q. 52 (page 603)

In Problems 47–52, find the unit vector in the same direction as $v$ : $v = 2 i - j$

Short Answer

Expert verified

The unit vector in the same direction as $v$ is $\frac{2}{\sqrt{5}} i - \frac{1}{\sqrt{5}} j$

Step by step solution

Step 1. Magnitude of the Vector

The given vector is $v = 2 i - j$

The magnitude of the given vector is $\sqrt{2^{2} + 1^{2}} = \sqrt{4 + 1} = \sqrt{5}$

Step 2. Unit Vector in the direction of v

Now, we multiply the scaler $\frac{1}{| v |} = \frac{1}{\sqrt{5}}$

A unit vector in the same direction as $v$ is $\frac{v}{‖ v ‖} = \frac{2 i - j}{\sqrt{5}} = \frac{2}{\sqrt{5}} i - \frac{1}{\sqrt{5}} j$

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In Problems 47–52, find the unit vector in the same direction as $v$ : $v = 2 i - j$

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=2i-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

Decision Maths

Statistics

Discrete Mathematics

Mechanics Maths

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 47–52, find the unit vector in the same direction as $v$ : $v = 2 i - j$