   Chapter 12, Problem 57RE

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# Finding the Arc Length of a Curve in Space In Exercises 59-62, sketch the space curve and find its length over the given interval. r ( t ) = − 3 t i + 2 t j + 4 t k , [ 0 , 3 ]

To determine

To Graph: The space curve and also calculate its length over the interval [0,3].

Explanation

Given: r(t)=3t i+ 2t j^+ 4t k^,  [0,3]

Graph: The vector equation can be rewritten as r(t)=(0.i^+0.j^+0.k^  )+(3i^+2j^+4k^  )t

This is a vector equation of a straight line passing through the point (0.i^+0.j^+0.k^  ) and parallel to the vector (3i^+2j^+4k^ ).

The graph of this line, all that need to plot the point and then sketch in the parallel vector.  In order to sketch, will assume that the vector is on the line and will start at the point in the line

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