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CE Suppose that each component of a certain vector is doubled.(a) By what multiplicative factor does the magnitude of the vectorchange? (b) By what multiplicative factor does the direction angleof the vector change?

a) 2 $\mathrm{A}$b) $\theta$

Physics 101 Mechanics

Chapter 3

Vectors in Physics

Physics Basics

Cornell University

University of Michigan - Ann Arbor

University of Washington

University of Winnipeg

Lectures

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in this problem will be looking at the fundamental properties of a vector. Here I've drawn a typical victor and read. It has an X component of three units in a one component of two units. Now its opponents that we have a second vector that has each of the components doubled from the red factor here. I'll actually draw it angry. So now you see that the ex direction is six units in the wind direction is four units in the first part of the problem that asked by what multiplication factor does the magnitude of the vector change? Since each of the components of the risk factor has an increased by a factor of two, the magnitude will also increase by a factor of two. So here we have a two factor increase in the magnitude now part B it as what's the multiplication factor in the angle direction of the vector from red to green? Here I'll draw that angle of the ref actor by fate in the Green Vector by five. I noticed that even though we increased each component of the red vector by two, the angle's data and find remained the same. Therefore, for the second part of the problem, we see a multiplication factor of one

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