Analytic Geometry — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

3 (c) Let L1 and La be the lines L2:x=2+t,y=3+4t,z=4+2t, show that the lines Ly and L intersect, and find their point of intersection. 4(a) Find the orthogonal projection of ü = i + j + k on b = 2i + 2j, and then find the vector component of i orthogonal to b. 4(b) Find an equation for the line L of intersection of the planes 4(c) Find an equation of the plane through (-1,4, - 3) that is perpendicular to the line x-2=t,y +3 = 2t, z=-t. 5 (a) Find the equation of the sphere passing through the points (1,0,0), (0,2,0), (0,0,3) and 5 (b) Find the equation of the circle of intersection of the sphere x? + y? + z? = 16 and the plane x + z = 4. 5 (c) Find the equation of the sphere through the circle x+y? +22 = 25, x + = = 5 and passing through the point (1,2,3). 6 (a) Find the equation of a cone with vertex (1, - 2,3) and base, the circle x2 + y? = 4 in the plane z = 0. 6 (b) Find the equation of the right circular cone which contains the three coordinate axes as generators. 6 (c) Find the equation of the cylinder whose generators are parallel to (2,1, - 2) and which passes through the circle x? + 2? = 9, y = 0.