Question: A cube has vertices at the eight points (x, y, z), where each of x, y, and z is either 0 or 1. (a) Find

A cube has vertices at the eight points (x, y, z), where each of x, y, and z is either 0 or 1.
(a) Find the general equations of the planes that determine the six faces (sides) of the cube.
(b) Find the general equation of the plane that contains the diagonal from the origin to (1, 1, 1) and is perpendicular to the xy-plane.
(c) Find the general equation of the plane that contains the side diagonals referred to in Example 1 .22.

Step by Step Solution

★★★★★

3.35 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Using Figure 134 in Section 12 for reference we will find a normal vector n and a point vector p for each of the sides then substitute into n x n p to ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

859-L-A-L-S (2182).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Suppose that the joint distribution of X and Y is uniform over a set A in the xy-plane. For which of the following sets A are X and Y independent? a. A circle with a radius of 1 and with its center...

In the three parts of Fig. 1.8, eight points are equally spaced and marked on the circumference of a given circle. (a) For parts (a) and (b) of Fig. 1.8 we have two different (though congruent)...

A cube has four diagonals. Show that no two of them are perpendicular.

1 of 40 2.5 Points The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds? A. 10...

2.5 Points Question 1 of 40 Give the order of the following matrix; if A = [aij], identify a32 and a23. 1 -5 e 0 7 -6 - -2 1/2 11 -1/5 A. 3 * 4; a32 = 1/45; a23 = 6 B. 3 * 4; a32 = 1/2; a23 = -6 C. 3...

1. [-/0.5 Points] DETAILS LARCALC11 15.8.007. Use Stokes's Theorem to evaluate F . dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with...

1 of 40 2.5 Points Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 8x + 5y + 11z = 30 -x - 4y + 2z = 3 2x - y + 5z = 12 A. {(3 -...

Question 1 of 40 2.5 Points Give the order of the following matrix; if A = [a ij ], identify a 32 and a 23 . 1 0 -2 -5 7 1/2 -6 11 e - -1/5 A. 3 * 4; a 32 = 1/45; a 23 = 6 B. 3 * 4; a 32 = 1/2; a 23...

question (b). plea 12. Build the range graph for each of the following mountain ranges and use the graph to find a solution to the problem in Example 4 Example 4: Mountain Climbers Puzzle Two people...

1. Use Cramer's Rule to solve the following system. x+y+z=0 2x - y + z = -1 -x + 3y - z = -8 A. {(-1, -3, 7)} B. {(-6, -2, 4)} C. {(-5, -2, 7)} D. {(-4, -1, 7)} 2. Use Gaussian elimination to find...

The Arcadia Manufacturing Company, based in Arcadia, Florida, is one of the fastest-growing companies in its industry. According to Ms. Prinze, the company's production vice president, keeping...

Refer to Figure 13-3. Suppose the economy is at long-run equilibrium point C. Suppose investors become pessimistic about their future of investment. Our analysis will be based on this pessimistic...

The cost of capital equals 1 0 percent. Assume that the cash flows occur in perpetuity. Conduct a sensitivity analysis of the project s NPV to variations in costs. ( Answers appear in order: [...

You are the project manager of the HQQ Project and youre working with your customer stakeholder. The stakeholder has asked that you find a method to reduce the overall project duration for her...

Let T : V W be a linear transformation between finite-dimensional vector spaces V and W. Let B and C be bases for V and W, respectively, and let A = [T] CB . Use the results of this section to give...

Use Theorem 6.2 to determine whether W is a subspace of V. V = D, W = {f in D : f (x) 0 for all x}

Use Theorem 6.2 to determine whether W is a subspace of V. V = F, W is the set of all integrable functions

AFW Industries has 188 million shares outstanding and expects earnings at the end of this year of $687 million. AFW plans to pay out 57% of its earnings in total, paying 31% as a dividend and using...

As a new junior analyst for a large brokerage firm, you are excited to demonstrate the skills you learned in college and prove that you are worth your attractive salary. Your first assignment is to...

What is the purpose of a printer's memory?To purge unwanted information from the printerTo assemble the way in which the images will be placed on paperTo store the document for future useTo remember...