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High School Math Calculus Precalculus with Limits: A Graphing Approach

A unit vector in the direction of u = 3 i − 4 k .

A unit vector in the direction of u = 3 i − 4 k .

Precalculus with Limits: A Graphing Approach

Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 10.2, Problem 34E

(a)

To determine

To find: A unit vector in the direction of u=3i−4k .

(a)

Expert Solution

Answer to Problem 34E

The unit vector in the direction of u=3i−4k is 15(3i−4k) .

Explanation of Solution

Given information:

The given vector is u=3i−4k .

Formula used:

The unit vector in the direction of vector u is v=u‖u‖ .

Calculation:

Use the formula for magnitude of vector u=u1i+u2j+u3k .

‖u‖=u12+u22+u32

Substitute 3 , 0 , −4 for u1 , u2 , u3 respectively in the formula.

‖u‖=u12+u22+u32=(3)2+(0)2+(−4)2=9+0+16=25=5

Therefore, the magnitude of vector u=3i−4k is 5 .

Substitute u=3i−4k for u and 5 for ‖u‖ in the formula.

v=u‖u‖=3i−4k5=15(3i−4k)

Therefore, the unit vector in the direction of u=3i−4k is 15(3i−4k) .

(b)

To determine

To find: A unit vector in the direction opposite of u=3i−4k .

(b)

Expert Solution

Answer to Problem 34E

The unit vector in the direction opposite of u=3i−4k is −15(3i−4k) .

Explanation of Solution

Given information:

The given vector is u=3i−4k .

Formula used:

The unit vector in the direction of vector u is v=−u‖u‖ .

Calculation:

As solved in part(a), The unit vector in the direction of u=3i−4k is v=15(3i−4k) . So, the unit vector in the direction opposite of u=3i−4k is −v=−15(3i−4k) .

Therefore, the unit vector in the direction opposite of u=3i−4k is −15(3i−4k) .

Chapter 10.2, Problem 33E

Chapter 10.2, Problem 35E

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - 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