Question: Question 4 [20 marks] (a) Lines L1 and L2 have vector equations r=5i2j6k+A(ijk), AER, r=5ij+lOk+,u(2i-l3j+4k), MGR, respectively. (i) Find the Cartesian equation of the plane

Question 4 [20 marks] (a) Lines L1 and L2 have vector equations r=5i2j6k+A(ijk), AER, r=5ij+lOk+,u(2i-l3j+4k), MGR, respectively. (i) Find the Cartesian equation of the plane that contains L1 and is parallel to L2. (ii) Find points A in L1 and B in L2 such that the line segment AB is perpendicular to both L1 and L2. (b) Let A(3, 2, 2), B(2, 5, 9) and C(4, 1, 2) be points in R3. (i) Find the exact value of the area of AABC'. (ii) Find the projection of the point (4, 3, 5) onto the plane containing A, B and 0. Question 5 [20 marks] (a) Solve the quadratic equation 2:2 (4 + 22);: 13 + 342' = 0. 1\\/i 50 (b) Express ( 1 + 2' ) in the form a + bi, where a, b E R. (e) Let A, B, C, D, E, F, G, H be the vertices of a regular octagon as shown in the following gure. It is given that A is at (1,3) and B is at (0,1). Find the coordinates of F

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