Answered: Vectors: a.) Can you find two vectors…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Vectors:

a.) Can you find two vectors with different lengths that have a vector sum of zero?
Explain your answer in detail.

b.) Can the magnitude of an object’s displacement be larger than the distance it has
traveled? What is the condition for them being equal. Explain your answers in detail.

Expert Solution

Step 1: Vector sum of two vectors:

$text a) Let two vectors: end text a with rightwards arrow on top equals a subscript x i with hat on top plus a subscript y j with hat on top b with rightwards arrow on top equals b subscript x i with hat on top plus b subscript y j with hat on top text And vector sum: end text c with rightwards arrow on top equals a with rightwards arrow on top plus b with rightwards arrow on top equals open parentheses a subscript x plus b subscript x close parentheses i with hat on top plus open parentheses a subscript y plus b subscript y close parentheses j with hat on top equals 0 i. e. a subscript x equals negative b subscript x a subscript y equals negative b subscript y text As component magnitude is same, two vectors will also have the same magnitude or length, end text text So, its not possible for two different length vectors to have a vector sum of zero. end text$

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