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Thursday, October 6, 2011
Page 1 CODE 111 Mathematics 1229A
PART A (18 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS IN PART A MUST BE
INDICATED ON THE SCANTRON SHEET. YOU SHOULD ALSO CIRCLE
YOUR ANSWERS IN THIS BOOKLET.
Use the following for questions 1, 2 and 3.
Let u= (1,0,−2) and v= (0,1,3).
mark Find 3u+ 2v.
A: (2,3,5) B: (2,1) C: (3,2,0) D: (3,2) E: (1,2,0)
mark Find u•v.
A:−6B: 6 C: (0,0,−6) D:−4E: 0
mark Find u×v.
A: (2,3,1) B: (2,−3,1) C: (0,0,−6) D: (−2,3,−1) E:−6
mark Find the magnitude (length) of u= 4i−3j.
A: 5 B: 25 C:√7D: 7 E:±5
mark Find all values of csuch that the vector u= (c, 1,−c, 0) is a unit vector.
A: any real value B:1
C: 1 D: 0 E: no real values
mark Find the unit vector that has the same direction as u= (1,0,1).
√2B: (1,0,1) C:1
√2D: (0,1,0) E:i
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Test 1 CODE 111 Thursday, October 6, 2011
mark Find all values of ksuch that the vectors u= (1, k) and v= (2, k) are orthogonal.
A: any real value B:√2C:−√2D: 0 E: no real values
mark Find all values of asuch that the vectors u= (1,0, a) and v= (a, 0,1) are collinear.
A: any real value B: 1 and −1C: 1 D: 0 E: no real values
mark Find the area of the triangle which has one vertex at the origin and has the other two
vertices at the points A(1,1,1) and B(1,0,1).
mark Let u,vand wbe vectors in R3and let cbe a scalar. Which of the following operations
A: (ii), (iii) and (iv) only B: (i), (ii) and (v) only C: (ii) and (iv) only
D: (ii), (iv) and (v) only E: All of them.
mark Find a standard form equation of the plane through the point P(1,0,0) with normal vector
A:y−2z= 0 B:x= 1 C:x= 0 D:x+ 2y+z= 0 E:x+ 2y+z= 1
mark For what value of tdoes the line x(t) = (1,1,1) + t(0,1,0) yield the point P(1,−1,1)?
A:−2B: 0 C: 2 D:−1E:Pis not on the given line
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