Ch15_review_sheet

Ch15_review_sheet - ~ k meters from point A. 7. Find the...

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Ch 15 Review Sheet Algebra II Honors – Mr. Petach Please write your answers on a separate sheet! 1. Find the cross product ~a × ~ b for each of the following vectors. Use the determinant method and the distributive property method for each set of vectors. (a) ~a = 2 ~ i + 3 ~ j , ~ b = 3 ~ i - 2 ~ j + 5 ~ k (b) ~a = 7 ~ i - 3 ~ j + 2 ~ k , ~ b = - ~ j + 3 ~ k 2. Find the projection of the vector ~v = 5 ~ i + 3 ~ j - 4 ~ k on the line that contains the vector ~ r = 2 ~ i + 4 ~ j . 3. Find the angle between the vectors ~a = 7 ~ i - 3 ~ j + 2 ~ k and ~ b = - ~ j + 3 ~ k . 4. Find the plane that contains the vectors ~a = 2 ~ i + 3 ~ j , ~ b = 3 ~ i - 2 ~ j + 5 ~ k and the point (2 , 3 , 5). 5. Find the equation of the plane that has a normal vector ~ b = 3 ~ i - 2 ~ j + 5 ~ k and contains the point (3 , - 5 , 7). 6. Find the moment force at point A if a force ~ F = 17 ~ i - 2 ~ j + 5 ~ k Newtons is acting at a distance ~ d = 2 ~ i + 4
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Unformatted text preview: ~ k meters from point A. 7. Find the work done if a force of 15 Newtons at an angle of 30 degrees (above horizontal) moves a box 10 meters along an incline that is 20 degrees (above horizontal). Draw a picture! 8. Find the equations of the planes that are parallel and a distance of 2 units from the plane 4 x + 8 y-z + 12 = 0. 9. Find the equation of the plane containing the points (1 , 2 , 3), (-2 , 3 , 6) and (2 , 6 ,-10) using the method of cross product. 10. Find the angle between the lines: L 1 x = 1 + 3 t y = 2-4 t z = 3 + 5 t L 2 x = 1 + 4 t y = 2 + t z = 3 + 2 t 1...
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This note was uploaded on 05/13/2011 for the course MATH 101 taught by Professor Impemba during the Fall '10 term at Grand Valley State.

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