Vector addition using geometry Vector addition using geometry is accomplished by
ID: 1956134 • Letter: V
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Vector addition using geometry Vector addition using geometry is accomplished by placing the tail of one vector, in this case B, at the tip of the other vector, A (Intro 1 figure) and using the laws of plane geometry to find C = root A^2 + B^2 - 2ABcos(c) and b = sin^ -1 (Bsin(c)/C), where the length C and angle are those of the resultant (or sum) vector, C. Vector addition using components Vector addition using components requires that a coordinate system be chosen. Here, the x axis is chosen along the direction of A (Intro 2 figure) . Given the coordinate system, the x and y components of B are B cos(theta) and Bsin(theta), respectively. Therefore, the x and y components of C are given by the equations Cx = A + Bcos(theta) and Cy= Bsin(theta). Part A Which of the following sets of conditions, if true, would show that Equations 1 and 2 above define the same vector C as Equations 3 and 4? Check all that apply. The two pairs of equations give the same a length and direction for C. b length and x component for C. c direction and x component for C. d length and y component for C. e direction and y component for C. f x and y components for C.Explanation / Answer
Use first principles. What is the definition of a vector. A vector is something that has magnitude and direction: a.) length and direction : that is certainly the definition of a vector b.) length and x-component: I can make the y-component positive or negative and it should not affect the length nor the y-component c.) Given direction and x component, length and y-component will be unique d.) length and y-component: same thing as b.) e.) direction and y-component of C: same reason as c.) f.) a unique x and y component will yield a unique length and a unique direction. Your answers should be: a,c,e,f
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