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Chapter 9: Problem 72

Use a computer algebra system to graph the plane. $$ 2 \cdot 1 x-4.7 y-z=-3 $$

Short Answer

Expert verified
Given the plane equation \(2x - 4.7y - z = -3\), the graph can be plotted by using a computer algebra system by first rearranging to give \(z = 2x - 4.7y + 3\). Then choosing a range for x and y to observe the plot.

Step by step solution

01

Rearranging the equation

We want to make z the subject of the formula to ease our understanding of the plane graph. This gives us the equation \(z = 2x - 4.7y + 3\)
02

Define the range of x and y

It is important to define the ranges of x and y when plotting the plane. Here we will use x and y in the range of -10 to 10. This range is chosen arbitrarily, but you can choose other ranges as necessary.
03

Graphing the plane

Using a computer algebra system such as Wolfram Alpha or Desmos, type in \(z = 2x - 4.7y + 3\) and set the range for x and y (e.g., -10 to 10). Observe the output graph of the plane.

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Most popular questions from this chapter

Let \(\mathbf{u}=\mathbf{i}+\mathbf{j}, \mathbf{v}=\mathbf{j}+\mathbf{k},\) and \(\mathbf{w}=a \mathbf{u}+b \mathbf{v} .\) (a) Sketch \(\mathbf{u}\) and \(\mathbf{v}\). (b) If \(\mathbf{w}=\mathbf{0}\), show that \(a\) and \(b\) must both be zero. (c) Find \(a\) and \(b\) such that \(\mathbf{w}=\mathbf{i}+2 \mathbf{j}+\mathbf{k}\). (d) Show that no choice of \(a\) and \(b\) yields \(\mathbf{w}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k}\).

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