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Page 1 CODE 111 Mathematics 1229A

Test 1

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).

1.1

mark Find 3u+ 2v.

A: (2,3,5) B: (2,1) C: (3,2,0) D: (3,2) E: (1,2,0)

2.1

mark Find u•v.

A:−6B: 6 C: (0,0,−6) D:−4E: 0

3.1

mark Find u×v.

A: (2,3,1) B: (2,−3,1) C: (0,0,−6) D: (−2,3,−1) E:−6

4.1

mark Find the magnitude (length) of u= 4i−3j.

A: 5 B: 25 C:√7D: 7 E:±5

5.1

mark Find all values of csuch that the vector u= (c, 1,−c, 0) is a unit vector.

A: any real value B:1

√2

C: 1 D: 0 E: no real values

6.1

mark Find the unit vector that has the same direction as u= (1,0,1).

A:1

√2,0,1

√2B: (1,0,1) C:1

√2,1

√2D: (0,1,0) E:i

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Mathematics 1229A

Test 1 CODE 111 Thursday, October 6, 2011

Page 2

7.1

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

8.1

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

9.1

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).

A:√6

2B:√2C:√6D:√2

2E: 1

10.1

mark Let u,vand wbe vectors in R3and let cbe a scalar. Which of the following operations

are deﬁned?

(i)c+u(ii)cu(iii)u×(v•w)

(iv) (u×v)•w(v)u•(v•w)

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.

11.1

mark Find a standard form equation of the plane through the point P(1,0,0) with normal vector

n= (1,2,1).

A:y−2z= 0 B:x= 1 C:x= 0 D:x+ 2y+z= 0 E:x+ 2y+z= 1

12.1

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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