Quiz 0- answer - evaluation Quiz PDF

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CONCORDIA UNIVERSITY FACULTY OF ENGINEERING AND COMPUTER SCIENCE AERO482/ENGR 6461 – Avionics Navigation Systems Pre-requisites Quiz Professor: Luis Rodrigues Date: September 18, 2017 ______________________________________________________________________________ Answer all questions.

Closed book exam. Total time: 30 minutes Good luck ! ______________________________________________________________________________

Problem 1 (Vector Calculus) An inertial reference frame {I } has fixed within it a reference point I and a set of unit vectors    ei1 , ei2 , ei3 . In this frame there are two vectors described as

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    s1 = ei1 − 2 ei2 − ei3     s2 = 2 ei1 + ei2 + ei3

 1. What is the norm of s1 ?

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T  2. What are the coordinates of s2 in frame {I } ? !" 2 1 1 #$   3. What is the component of s1 along the direction ei3 ? -1  s   4. What is the projection of vector s1 into vector s2 ? − 2 6   5. What is the angle between s1 and s2 ? 99.6 degrees        6. Compute s1 ⋅ s2 and s1 × s2 . -1 and − ei1 − 3ei2 + 5ei3   7. Are s1 and s2 orthogonal vectors ? Why ? No because their dot product is not zero.

Problem 2 (Probability) Suppose that you throw two dice at the same time and associate a random variable X to the outcome of the first die and a random variable Y to the outcome of the second die Answer the following questions: 1. What is the probability that both dice will have different results, i.e, P(X ≠ Y) ? 5/6 2. What is the probability that X+Y is even ? 1/2 3. Compute the expected value of [X Y]. [3.5 3.5]

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