a. List out three most widely used coordinate systems. With the aid of diagrams, discuss the differences between the thr

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A List Out Three Most Widely Used Coordinate Systems With The Aid Of Diagrams Discuss The Differences Between The Thr 1 (63.19 KiB) Viewed 34 times

a. List out three most widely used coordinate systems. With the aid of diagrams, discuss the differences between the three named coordinate systems. [10 Marks] b. Two vectors with dimensions A = 5i + 3j + k and B = 4i+j+ 2k are used for the following calculation. Determine: i. ii. iii. iv. The dot product A. B. [2 marks] [3 Marks] The angle between vectors A and B. The cross product A xB. [2 marks] The area of the parallelogram spanned by the vectors A and B. [3 Marks] c. Find the product AB where A and B are matrices given by: A = 12 [1 3 51 [2 4 6 [36] B = 1 4 5 2. [10 Marks] d. With the aid of a diagram, find the volume of the solid of revolution obtained by revolving the area below the graph of y = x - 4x³, the x-axis and y ≥ 0 about the x-axis. Hint: key the term x - 4x³ to google search for the diagram. e. Solve for the following system of linear equations by Cramer's rule, x₁ + x₂ = x3 = 4 x₁2x₂ + 2x3 = -5 2x₁x₂ + 2x3 = -2 [10 Marks] [10 Marks]