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# (a) Is the vector a unit vector Justify your answer. (b) ## Problem 44E Chapter 1

University Physics | 13th Edition

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Problem 44E

(a) Is the vector a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case justify your answer. (c) If where a? ? is a constant, determine the value of a that makes a unit vector.

Step-by-Step Solution:

Solution 44E Problem (a) Step 1: Consider a =i + j + k ˆ The given vector is not a unit vector, because modulus of unit vector must be equal to 1. Proof 2 2 2 | | 1 + 1 + 1 | | 1 + 1 + 1 | | 3 The given has the modulus greater than unity, hence it is not a unit vector Problem (b) Step 1: The unit vector can not have the components greater than 1. Justification Sum of squares of vector components will be having magnitude greater than 1. Even if we take square root of the value found, we can not get value equal to 1. EX. consider vector 2i +3 j + 4kˆ 2 2 2 Modulus of the vector taken = 2 + 3 + 4 = 4 + 9 + 16 modulus = 29 which is greater than 1. Hence unit vector can not have magnitudes greater than 1. Step 2: The unit vector can have negative components. Justification 3 ˆ 4 ˆ Take a vector a = i 5 5 j 2 2 Modulus of the above vector = ( 5 + ( )45 9 16 = 25+ 25 25 = 25 modulus = 1 Since the modulus of the vector taken is 1, we can say that the unit vectors can have negative components. Problem ( c ) Step 1: Given vector A = a (3.0i + 4.0j ) Where a is constant In order to make vector as unit vector, modulus of A must be equal to 1. Step 2: ˆ ˆ A = a (3.0i + 4.0j ) A =3.0ai + 4.0ajˆ (3a) + (4a)2 Therefore modulus of = 2 2 = 9a + 16a 2 Taking a outside the square root = a 9 + 16 = a 25 Modulus of A = 5a2

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##### ISBN: 9780321675460

This full solution covers the following key subjects: Vector, unit, any, components, Answer. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. This textbook survival guide was created for the textbook: University Physics, edition: 13. University Physics was written by and is associated to the ISBN: 9780321675460. The answer to “(a) Is the vector a unit vector? Justify your answer. (b) Can a unit vector have any components with magnitude greater than unity? Can it have any negative components? In each case justify your answer. (c) If where a? ? is a constant, determine the value of a that makes a unit vector.” is broken down into a number of easy to follow steps, and 53 words. Since the solution to 44E from 1 chapter was answered, more than 327 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 44E from chapter: 1 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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