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Homework:MML05: 14.1

Multiple fill-in-the-blank

Part 1Find a function Bold r left parenthesis t right parenthesisr(t) for the line passing through the points Upper P left parenthesis 0,0,0 right parenthesisP(0,0,0) and Upper Q left parenthesis 2,4,1 right parenthesisQ(2,4,1). Express your answer in terms of Bold ii, Bold jj, and Bold kk. Part 1Bold r left parenthesis t right parenthesisr(t)equals=2tBold iiplus+left parenthesis nothing right parenthesis Bold j[input]enter your response here jplus+left parenthesis nothing right parenthesis Bold k[input]enter your response here k, for [input]enter your response here [input] ▼ less than or equals≤ less than< empty selection t [input] ▼ less than or equals≤ less than< empty selection [input]enter your response here

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Step-by-Step Analysis

We start by identifying the two given points that determine the line: P(0,0,0) and Q(2,4,1). The direction vector of the line is found by subtracting P from Q, giving <2,4,1>. This means any point on the line can be written in vector form as r(t) = t<2,4,1> if we use t as the scalar para......Login to view full explanation

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