Coordinate Geometry and vector analysis

Daffodil International University Department of Electrical and Electronic Engineering Faculty of Engineering Midterm Examination, Fall – 2026 Course Code: 0541-131 Course Title: Coordinate Geometry and Vector Analysis Section: A, B Level-Term: L1-T3 Teacher's Initial: IJM Full Marks: 25 Exam Date: 28th October, 2026 Time: 1.5 Hours *** Answer all the following questions sequentially. [The second right most column indicates the course outcomes (COs) with respective Bloom's level and the right most column indicates the allocated marks.] Q1. (a) Describe the relation between 3-D system. CO-1 (C2) [02] (b) Convert the following cylindrical coordinates (4√3, 45°, 60°) into rectangular coordinates. CO-1 (C2) [02] Q2. (a) Explain homogeneous equation and Demonstrate the equation of the bisectors of an angle produced by the pair of straight line represented by the equation 8x^2 – 42xy – 11y^2 = 0 at origin. CO-1 (C2) [03] (b) Interpret the equation to the standard form 32x^2 + 52xy – 7y^2 – 64x – 52y – 148 = 0 CO-1 (C3) [05] Q3. (a) Remove the first degree term in 2x^2 + 5y^2 – 12x + 10y – 7 = 0. CO-1 (C2) [03] (b) Determine the equation of the Parabola x^2 – 2xy + y^2 + 2x – 4y + 3 = 0 after rotating of axes through 45°. [03] Q4. (a) Interpret the equation of the plane passing through the lines of intersection of the plane 2x – y = 0 and 3z – y = 0 and perpendicular to the plane 4x + 5y – 3z + 1 = 0. CO-1 (C2) [03] (b) Illustrate the equation of the plane which is parallel to the plane 4x-4y+7z-3=0 and distance 4 units from the points (3, 1, -2). [04]