Purdue MA 26100 - MA261PracticeProblems (8 pages)

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MA261PracticeProblems



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MA261PracticeProblems

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Pages:
8
School:
Purdue University
Course:
Ma 26100 - Multivariate Calculus
Multivariate Calculus Documents

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MA 261 PRACTICE PROBLEMS 1 If the line has symmetric equations y x 1 z 2 2 3 7 nd a vector equation for the line 0 that contains the point 2 1 3 and is parallel to A r 1 2t i 3t j 2 7t k C r 2 2t i 1 3t j 3 7t k E r 2 t i j 7 3t k B r 2 t i 3 j 7 2t k D r 2 2t i 3 t j 7 3t k 2 Find parametric equations of the line containing the points 1 1 0 and 2 3 5 A x 1 3t y 1 4t z 5t C x 1 2t y 1 3t z 5t E x 1 t y 2 t z 5 B x t y t z 0 D x 2t y 3t z 5t 3 Find an equation of the plane that contains the point 1 1 1 and has normal vector 1 2 i 2j 3k A x y z 9 2 0 D x y z 0 B x 4y 6z 9 0 E 1 2 C x 1 1 2 y 1 2 z 1 3 x 2y 3z 1 4 Find an equation of the plane that contains the points 1 0 1 5 3 2 and 2 1 4 A 6x 11y z 5 D r 18 i 33 j 3 k B 6x 11y z 5 E x 6y 11z 12 C 11x 6y z 0 5 Find parametric equations of the line tangent to the curve r t t i t2 j t3 k at the point 2 4 8 A x 2 t y 4 4t z 8 12t B x 1 2t y 4 4t z 12 8t C x 2t y 4t z 8t D x t y 4t z 12t E x 2 t y 4 2t z 8 3t 6 The position function of an object is r t cos t i 3 sin t j t2 k Find the velocity acceleration and speed of the object when t Velocity Acceleration p Speed 4 A i 2 k 3 j 2 k p1 B i 3 j 2 k i 2 k p 10 4 2 2 C 3 j 2 k i 2 k p9 4 i 2 k D 3 j 2 k 9p 4 2 E i 2 k 3 j 2 k 5 1 7 A smooth parametrization of the semicircle which passes through the points 1 0 5 0 1 5 and 1 0 5 is A r t sin t i cos t j 5 k 0 t C r t cos t i sin t j 5 k 2 t 3 2 E r t sin t cos t j 5 k 2 t 3 2 B r t cos t i sin t j 5 k 0 t D r t cos t i sin t j



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