Q9 Q10 If x~ = -7i~+ 10j~ - 2k~, y~ = -9i~ - 11j~ - 3k and z = 2i~ + 9j~ + 8k~ ,

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Q10

If x~ = -7i~+ 10j~ - 2k~, y~ = -9i~ - 11j~ - 3k and z = 2i~ + 9j~ + 8k~ , find x middot y times z The answer is a vector or a scalar (but not both). Fill in all the boxes, putting NA in any boxes not applicable to the answer. Make sure you include the minus in any negative coefficients forget to enter zero in any box where calculation results in a zero answer. x middot y times z is the vector i~ + j~ k~ or x middot y times z is the scalar A first order linear differential equation has standard form dy / dx +f(x) middot y =g(x). Given the linear differential equation, dy / dx - 5 tan (2x) = 14xy, identify f(x), g(x) from the standard form of the equation and answer the multiple choice question. f(x) g(x) = Which of the following would you use in determining the integrating factor? Y 14x -y -14x -5 tan (2x) dy / dx

Explanation / Answer

y x z = -81 k - 72 (-j) - 22 (-k) -88 i - 6j -27 (i) = -115 i + 66 j - 59 k now x. (y x z) = ( -7i + 10 j - 2k).(-115 i + 66 j - 59 k) = 805 + 660 + 118 = 1583 a scalar dy/dx - 5 tan (2x) = 14 xy dy/dx - 14 xy = 5 tan (2x) dy/dx + f(x) .y = g(x) therefore f(x) = -14 x g(x) = 5 tan (2x) Integrating factor= e^int(f (x)dx) so f(x) is used which is option D -14x

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