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quiz0 - 1 Two vectors A and B are drawn as in the following...

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A B Quiz 0 Name: ID: Mathematics is the language in sciences. Certain amount of knowledge in mathematics is required to understand the material in this course. To help you check how well you are prepared in math for this course, please complete this quiz in class. The grade of this quiz will not be counted towards your final course grade. However if you find this quiz difficult, you may need to review your math text books. 1. In a Cartesian coordinate system, vector A = 2 i + 3 j + 4 k , vector B = 3 i + 4 j + 5 k . Here the vectors i, j and k are the unit vectors for the x-, y- and z- axes. Write the expression for vector C and scalar D if: (1) C = A + B (2) D = A · B (3) C = A × B 1. Solve the following equation for variable x , make sure to get all possible solutions.
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Unformatted text preview: 1. Two vectors A and B are drawn as in the following figure. Both are originated from point O . Vector C = A + B . Show vector C in the same figure. 1. The formula that links R with R 1 and R 2 is this: If R 1 = 2, R 2 = 3, what is the value of R ? 2 1 1 1 1 R R R + = 2 2 1 ) 9 ( 4 x x =-O 1. Solve the following equations for variables x, y and z . 1. If , What is ? 1. Solve this integral: 1. Solve the equation for q. The variable q is a function of t . Here R and C are constants. When 16 4 3 3 2 4 3 3 =-+ = +-= + + z y x z y x z y x x x x x y 1 ) ln( ) 6 sin( 3 2 + + + = dx dy ∫ ∞ = R r dr ) R ( U 2 . Q q , t = = = + dt dq R C q...
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