a) On a threedimensional axis, make a sketch of the position vector using a rectangular prism: 55 = (1,3,2) (2 marks) b) State the equation of the plane parallel to xyplane and passing Through the point (1,3,-2). (1 mark) Given a = ( 2,9,7)and i7 = 2? 33' , determine: the angle between the vectors. (2 marks) the vector projection of it onto \\7. (2 marks) ll] x 0" (2 marks) a unit vector perpendicular to both a and \\7 . (1 mark) Given the points A(3,2,0), B(1,0,1) and C(2,2,2) determine the vector equation of the line that contains the point(4,5,-1) and is perpendicular to the plane determined by the points A, B and C. (3 marks) If (16,m,n) is a point on the line in part a), find m and n. (1 mark) determine the Scalar equation of the plane that contains all three points A, B and C. (2 marks) Show that the lines Pi = (4, 7, 1)+ r(4, 8, 4) and F2\" = (1, 5, 4)+u( 1, 2, 3) intersect at right angles m find the point of intersection. (5 marks) 1. A pedicab is pulled a disTance of 300 m by a force of 110 N applied aT an angle of 6\"To The roadway. CalculaTe The work done. Provide a diagram. (2 marks) 2. An airplane has a speed of 300 km/h and is headed due wesT. A wind is blowing from The souTh aT 50 km/h. DeTermine The resulTanT velociTy of The airplane. Provide a SCALE diagram. (3 marks) 3. Find k such ThaT The plane kx + 2y - z = 7 is parallel To The line _X 11 = _Y E 2 = 2:13 _ (2 marks) PART C: COMMUNICATION 1. G and Gore boTh non-zero vecTors. How are U and relaTed if: a) G n?