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Chapter 9: Problem 10

Determine the location of a point \((x, y, z)\) that satisfies the condition(s). \(z=-3\)

Short Answer

Expert verified
The points that satisfy the given condition \(z = -3\) are all points on the plane \(z = -3\), and can be represented as \((x, y, -3)\) where \(x\) and \(y\) can be any real number.

Step by step solution

01

Understanding the dimensions

The point in three-dimensional space is defined by three coordinates: \(x, y, \) and \(z\). These represent a location in space. The given condition sets the \(z\)-coordinate to -3, which means the location of the point is somewhere on the plane where \(z = -3\).
02

Considering the range of possible points

Since \(x\) and \(y\) are not specified, they can take on any real value. Therefore, the point can be any point on the plane \(z = -3\). This means that there are infinitely many solutions.

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Most popular questions from this chapter

In Exercises \(51-56,\) find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(\mathbf{z}=\mathbf{u}-\mathbf{v}\)

Find the angle \(\theta\) between the vectors. $$ \begin{array}{l} \mathbf{u}=3 \mathbf{i}+2 \mathbf{j}+\mathbf{k} \\ \mathbf{v}=2 \mathbf{i}-3 \mathbf{j} \end{array} $$

In Exercises \(65-68,\) find the magnitude of \(v\). \(\mathbf{v}=\mathbf{i}-2 \mathbf{j}-3 \mathbf{k}\)

Let \(A, B,\) and \(C\) be vertices of a triangle. Find \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}\)

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