Solutions_-_Midterm_Test

Solutions_-_Midterm_Test - Concordia University Department...

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Concordia University Department of Electrical and Computer Engineering ENGR 233 : Applied Advanced Calculus Fall 2007 Mid-Term Exam Solution Time: 75 Minutes Question 1 : Express the vector in terms of the vectors a and shown in the following figures. x b Figure 1(a) Figure 1(b) Solution: In Figure 1(a): b a b) (a x = + = In Figure 1(b): b a b) (a x 2 2 2 = = Question 2 : Find a vector 1 , , y x = v that is orthogonal to both 1 , 1 , 3 = a and 2 , 2 , 3 = b . Solution: The equations of system are: ) 2 ( 0 2 2 3 ) 1 ( 0 1 3 L L L L L L L L L = + + = + y x y x Solving equations (1) and (2), we have 3 1 = y and 9 4 = x Hence, the vector is 1 , , 3 1 9 4 = v Question 3 : Find the volume of a parallelepiped for which the vectors a , b and given below are three edges. c k j i a + + = 3 and k j i b + + = 4 k j i c 5 + + = 1
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Solution: We have, k j i k j i k j i c b 3 4 19 1 1 4 1 5 1 1 1 5 1 1 4 5 1 1 1 4 1 = + = = × Hence, the volume of the parallelepiped is () () ( ) 50 3 4 57 3 4 19 3 = = + + = × k j i k j i c b a cu. units.
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Solutions_-_Midterm_Test - Concordia University Department...

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