SHORT QUESTIONS TEST COMPLEX NUMBERS AND VECTORS FIVE MINUTES READING TIME TEST TIME TOTAL: 70 minutes NON CALCULATOR [Maximum Marks: 6] Let = 312 , = 11 = 2228 (a) Find (b) Find the value of such that is parallel to [Maximum Marks: 6] Point has position vectors 3 + 2 . Point D lies on the line with equation = + 5 + ( + 2). Find the value of such that is parallel to the x-axis [Maximum Marks: 6] Two vectors are given by = and = 2 , where [0,2]. Find all possible values of for which are perpendicular. [Maximum Marks: 6] Three points have coordinates 3, 1, 1 , 4, 1, 3 3, + 1, + 1 , where > 0. (a) Find a vector perpendicular to both and . (b) Given that the area of the triangle is 6 2, find the value of .

[Maximum Marks: 5] Two unit vectors are given such that + 2 = | 2| (a) Find the value of (b) Hence find the angle between [Maximum Marks: 6] Does the line joining 1, 4, 3 (7,5,6) intersect the line !!!! = = !!!! ? If it does, find the point of intersection, if it does not then describe their relationship to one another. [Maximum Marks: 8] Two roots of the quantic equation: ! 7! + ! + ! + 150 = 0 (where , ) are 3 and 1+ 2 (a) Write down a third root of the equation (b) One of the remaining two roots is + . Show that ! + ! = 10 (c) Find the values of and (d) Hence, find the values of , [Maximum Marks: 6] Let = !!!! (a) Express in terms of (b) If = 1, show that = 1

[Maximum Marks: 8] (a) Show that !!"!!!!"! = (b) Find the value of cos (3) (c) Find the exact value of cos ( + 3) [Maximum Marks: 6] (a) If is a complex number ! + = , where k is real, show that either is real or = !! (b) If is not real, find the set of possible values for [Maximum Marks: 5] Show that ! is real