INSTRUCTIONS FOR THE QUESTIONS BELOW:

8 - Investigate Interaction of Three Planes / 2 marks Plot the following planes and the normal vectors of each plane. x - 2y + 32 = 4 2x - 4y + 62 = 15 3x - 6y + 92 = 1 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark) 9 - Investigate Interaction of Three Planes / 2 marks Plot the following planes and the normal vectors of each plane. x + 6y 4- 32 = 8 6x+36y+181 = -39 2x + 12y+62= 16 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark) . Show all steps fully and use proper notation (e.g. for vectors, do product, and cross product). . Write the nal solution in the simplest form and put a box around it. Write the direction and normal vectors in the lowest terms (preferably without any fractions and using positive direction numbers). Give exact answers unless explicitly asked to provide an approximate answer . In order to earn full marks, students must show all their work and present complete solutions with sufcient explanation. . Be prepared to demonstrate and explain any of your solutions if requested. . For question requiring you to plot lines, planes, and vectors in R3\": a. Go to Geogebra 3D and plot the required vectors, lines, and planes. b. Change the color of each object (plane, line, normal) for better contrast c. Insert the screenshot of each plot! 3d visualization; disable the 'Show Plane' setting. Ensure the key features of the plan are visible in the screenshot. d. Provide a summary of the features of plot andfor intersection using appropriate terminology. 10 of 17 10 - Investigate Interaction of Three Planes / 2 marks Plot the following planes and the normal vectors of each plane. 2x 3y + z = -3 6x 9y + 32 = -9 -4x + 6y 22 = 6 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark) 11 - Investigate Interaction of Three Planes / 2 marks Plot the following planes and the normal vectors of each plane. x + 2y + 32 = 5 2x -3y + z = -15 2x 3y + z = 9 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark) 12 - Investigate Interaction of Three Planes / 2 marks Plot the following planes and the normal vectors of each plane. 3X - 2y + 32 = -3 3X + 4y - 62 = 5 2X 3y + 2 = 1 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark) 13 - Investigate Interaction of Three Planes /2 marks Plot the following planes and the normal vectors of each plane. X + 2y + 32 = 4 X y 32 = 8 X + 5y + 92 = -16 Describe the interaction of these planes using appropriate terms. How many solutions does this system have? Describe the solution. (1 mark) State the normals of all planes and write them in the lowest terms. Insert the plot and feel free to provide a link.. (1 mark)