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please help with the following questions 8. The following system of equations represents three planes that intersect in a line. Therefore, the system is (1
please help with the following questions
8. The following system of equations represents three planes that intersect in a line. Therefore, the system is (1 mark) In the following sub questions your goal is to lead me through your thought process in finding the solution to this system of equations (the infinite number of points along the line in which the planes intersect). x-y-32--2 x - 3y - 2z = -2 x + 5y - 62 = -2 a) What analysis would you FIRST do to narrow down the possible scenarios of these planes to the triangular prism, the pinwheel, or the point? (1 mark) b) Perform a test to show that the three planes do NOT intersect at a point. This is because the planes' normal vectors are (3 marks) c) Show how you would know for sure that the planes intersect in a line and that the triangular prism scenario does NOT result. Explain why this is so along side your calculations in your solution. (6 marks) d) Finally, solve the system of equations and state a vector equation for the line in which the three planes intersect. (5 marks) 9. Find the angle between adjacent triangular sides of a square based pyramid whose height is equal to the length of the base sides. (2 marks) 8. The following system of equations represents three planes that intersect in a line. Therefore, the system is (1 mark) In the following sub questions your goal is to lead me through your thought process in finding the solution to this system of equations (the infinite number of points along the line in which the planes intersect). x-y-32--2 x - 3y - 2z = -2 x + 5y - 62 = -2 a) What analysis would you FIRST do to narrow down the possible scenarios of these planes to the triangular prism, the pinwheel, or the point? (1 mark) b) Perform a test to show that the three planes do NOT intersect at a point. This is because the planes' normal vectors are (3 marks) c) Show how you would know for sure that the planes intersect in a line and that the triangular prism scenario does NOT result. Explain why this is so along side your calculations in your solution. (6 marks) d) Finally, solve the system of equations and state a vector equation for the line in which the three planes intersect. (5 marks) 9. Find the angle between adjacent triangular sides of a square based pyramid whose height is equal to the length of the base sides. (2 marks) Step by Step Solution
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