ES 183 June 2017 Exam Questions

ES1830


THE UNIVERSITY OF WARWICK


First Year Examinations: Summer 2017


ENGINEERING MATHEMATICS AND SYSTEMS MODELLING




Candidates should answer the THREE COMPULSORY QUESTIONS.


Time Allowed : 3 hours.


Only calculators that conform to the list of models approved by the School of Engineering may
be used in this examination. The Engineering Databook and standard graph paper will be
provided.


Read carefully the instructions on the answer book and make sure that the particulars required are
entered on each answer book.

USE A SEPARATE ANSWER BOOK FOR EACH SECTION

, ES1830




SECTION A: ENGINEERING MATHEMATICS

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1.

(i) In the square ABCD, shown in Fig. 1, two vectors are defined as 𝒑 = ⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗ . Find a
𝐴𝐵 and 𝒒 = 𝐵𝐶
vector expression that represents the diagonal ⃗⃗⃗⃗⃗⃗
𝐷𝐵 .




Fig. 1: The square ABCD
(2 marks)

(ii) Three vectors are given as:

𝒂 = 2𝒊 + 𝒋 + 3𝒌, 𝒃 = 3𝒊 + 2𝒋 + 4𝒌 and 𝒄 = 5𝒊 + 7𝒋 − 6𝒌 .

(a) Calculate the cross product 𝒂 × 𝒃 (3 marks)

(b) Calculate the triple product (𝒂 × 𝒃) ∙ 𝒄 (3 marks)
.

(iii) Write the plane 3𝑥 − 3𝑦 − 𝑧 = 14 in vector form. (2 marks)
.
𝑑𝑦
(iv) Find 𝑑𝑥 where


(a) 𝑦 = 𝑥 2 ln𝑥. (3 marks)

𝑛
(b) 𝑦 = √𝑥 2 + 1 , and where 𝑛 is a constant. (3 marks)


(c) 𝑦 2 + 𝑥 = 𝑥 3 + 3𝑦 (3 marks)




Question 1 Continued Overleaf
1