# 3 for the points a 1 4 1 b 3 5 2 and c 5 1 2 i find

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3. For the points A (1, 4, 1), B (3, 5, -2) and C (5, 1, 2), (i) Find cos (L BAG). (ii) F ind proj AC (A.8). Mark 4. In the plane with a cartesian co-ordinate system, let OACB be a parallelogram, with 0 the origin and GA= a, oB = b, where a ,}t b. (i) Write down (and label as such), parametric vector equations of the lines OC and AB in terms of a and b. (ii) Find the co-ordinates of the point P of intersection of lines OC and AB in terms of a and b. (iii) Show that 1 6P 1 = IPCI and 1.P1 = 1n1. Please write your answers on lined A4 paper and staple to this cover shee t .
UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS MATH1131 / 1141 Mathematics lA Algebra Sl 2014 TEST 1 VERSION 4a This sheet must b e filled i n and stapled to the front o f your answers Student's Family Name Initials Student Number Tutorial Code Tutor's Name Note: The use of a calculator is NOT permitted in this test Show all your working All answers should be given in the appropriately SIMPLIFIED form. QUESTIONS (Time allowed: 25 minutes) 1. For the points A (l, 2, 3), B (5, 7, -2) and C (8, -3, 2) in ffi.3; (i) Find the co-ordinates t of the point Ton AB such that AT= 2TB. Mark (ii) Find the co-ordinates d of the point D such that the quadrilateral ABCD (named in cyclic order) is a parallelogram. 2. Find a parametric vector equation for the plane in ffi.3 with cartesian equation Hence give two n o n - parallel non-zero vectors which are parallel to the plane. 4. Let C be the straight line in ffi.3 through the point P (1, 2, 3) and parallel to the vector v = (D. L et Q be the point with ccrordinates (1,4,4). (i) Find projv (?Q) · (ii) Find the shortest distance d between the line C and Q. (iii) Find the co-ordinates m of the point Mon P which is closest to Q. Please write your answers on lined A4 paper and staple to this cover sheet.
UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS MATH1131 / 1141 Mathematics lA Algebra Sl 2014 TEST 2 VERSION la I T his sheet must be filled in and stapled to the front of your answers J Student's Family Name Initials Tutorial Code Tutor's Name Note: The use of a calculator is NOT permitted in this test Show all your working All answers should be given in the appropriately SIMPLIFIED form. QUESTIONS (Time allowed: 25 minutes) l. For the complex numbers z = 1 + 5i, w = 3 - 2i calculate Im ( z + 3iw) , z / w , Arg ( l - 4i - w) in simplified cartesian form. Student Nu m ber [� Mark 2. Determine what conditions on bi, b,, b3, b4 are needed to ensure that ( t) belongs to the spM of the veclorn ( �;} ( �!) , OJ 3. Use the identity 1 'll ' ll sinB = 2i ( eiv - e - i" ) to write sin5 e in terms of sine' sin 2e' sin 3e' .... Please write your answers on lined A4 paper and staple to this cover sheet.
UNIVERSITY OF NEW SOUTH vVALES SCHOOL OF MATHEMATICS AND STATISTICS MATH1131 / 1141 Mathematics lA Algebra Sl 2014, TEST 2 VERSION lb This sheet must be filled in and stapled to the front of your answers Student's Family Name Initials Tutorial Code Tutor's Name Note: The use of a calculator is NOT permitted in this test Show all your working All answers should be given in the appropriately SIMPLIFIED form.
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