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Chapter 1: 10DQ (page 27)

Is the vector(i铃�+j铃�+k铃�) a unit vector? Is the vector(3.0i铃�-2.0j铃�) a unit vector? Justify your answers.

Short Answer

Expert verified

The vectors i铃�+j铃�+k铃� and3.0i铃�-2.0j铃� are not a unit vector.

Step by step solution

01

Introduction

Unit vectors are the vectors whose magnitude is exactly 1 unit. They are very useful for various reasons. Specifically, the unit vectors [0,1]and [1,0] can together form any other vector.

02

Explanation

Unit Vector 鈥� A unit vector is a vector with magnitude 1.

Let the vector a鈫�=i^+j^+k^.

Magnitude:

a鈬赌=12+12+12=3

Since magnitude is not 1, a鈬赌is not a unit vector.

Likewise, assume the vector b鈫�=3.0i^-2.0j^.

The amplitude of the vector is

b鈫�=32+22=9+4=13

Which is not equal to 1.

Hence, it is not a unit vector.

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