4 - Investigate Interaction of Two Planes / 2 marks Plot the following and their normal vectors. X + 6y + 32 = -8 2x + 12y + 62 = 8 Describe the interaction of these planes using appropriate terms. (0.5 mark) How many solutions does this system have? Describe the solution. (0.5 mark) State the normal of both planes and write them in the lowest terms. (0.5 mark) Include the plot below and feel free to provide a link. (0.5 mark) 5 - Investigate Interaction of Two Planes / 2 marks Plot the following and their normal vectors. x + 6y + 32 = 8 2x +12y+62= 16 Describe the interaction of these planes using appropriate terms. (0.5 mark) How many solutions does this system have? Describe the solution. (0.5 mark State the normal of both planes. (0.5 mark) Include the plot below and feel free to provide a link. (0.5 mark) 6 - Investigate Interaction of Two Planes / 2 marks Plot the following and also their normal vectors. X -3y + 22 = 11 X +3y+62 = 7 Describe the interaction of these planes using appropriate terms. (0.5 mark How many solutions does this system have? Describe the solution. (0.5 mark) State the normals of both planes and write them in the lowest terms. (0.5 mark) Include the plot below and feel free to provide a link. 7 - Find Intersection of Two Planes Algebraically /4 marks Find the solution for the intersection of the following two planes (if it exists). OthenNise show why the solution does not exist. (If it is a line, write the vector or parametric equation of the line). X-3y + 22 =11 x+3y+62 = 7 Solution (provide the solution in the correct form e.g. point or an equation): Show your work] reasoning below. 2- Vector Terms: Concisely dene the following terms (for a set of vectors) and how we can test for it. / 5 marks Coplanar Linearly independent Linearly dependent Orthogonal 3- Classify Vectors I 10 marks Analyze the following algebraic vectors. (Time estimate: '10 mins) a=(52,17) b:(3,,23) a) Are these vectors coplanar, collinear linearly independent? b) Are any pair or all three vectors orthogonal to each other? If so, which ones