Sketch the vectors r0 = 2, 0 and r1 = 1, 3, andthen sketch the vectors 13 r0 + 23 r1, 12

Chapter 11, Problem 41

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Sketch the vectors \(r_{0}=\langle-2,0\rangle\) and \(v=\langle 1,3\rangle\), and then sketch the vectors

    \(\frac{1}{3} r_{0}+\frac{2}{3} r_{1}, \frac{1}{2} r_{0}+\frac{1}{2} r_{1}, \frac{2}{3} r_{0}+\frac{1}{3} r_{1}\)

Draw the line segment \((1-t) r_{0}+t r_{1}(0 \leq t \leq 1)\). If  is a positive integer, what is the position of the point on this line segment corresponding to \(t=1/n\), relative to the points \((-2,0)\) and \((1,3)\)?

Equation Transcription:

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Text Transcription:

r_0=〈-2,0〉

v=〈1,3〉

1/3 r_0+2/3 r_1, 1/2 r_0+1/2 r_1, 2/3 r_0+1/3 r_1

(1-t)r_0+tr_1(0 <= t <= 1)

 t=1/n

(-2,0)

(1,3)