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Test1Review - and 11 Write an equation for the plane...

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MATH 234 MAKE YOUR OWN TEST 1 REVIEW Step 1: Insert appropriate points or equations into the following questions. 1. Perform the following vector operations for u = , v = , and w = . a. 2 u + 3 v b. | u + w | c. u · v d. u × v + 3 w 2. Find the angle between the vectors and . 3. Calculate the vector projection Proj v u . (This is likely to appear as word problem or in other prob- lems too) 4. Write the vector in (magnitude)(unit vector) form. 5. A force of is applied to a wrench at an angle of at distance from the bolt. Find the magnitude of the torque. What is the relationship between the direction of the torque and the force? 6. Find the area of the triangle (or parallelogram) with vertices , , and (and for parallelogram). 7. Write an equation for a line which passes through the two points and . 8. Write an equation for the plane containing the three points , , and . 9. Write an equation for the plane parallel to the plane and containing the point . 10. Write a parameterization for the line given by the intersection of the two planes
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Unformatted text preview: and . 11. Write an equation for the plane spanned by the two intersecting lines and . 12. Find the distance between the point and the line . 13. Show the following line and plane are parallel and then find the distance between them. 14. Sketch a graph of the (quadric or cylindrical) surface given by the following equation: . 15. Below are equations and graphs. For each equation, identify the correct graph. Step 2: Insert real-world things into two of the above questions to make them word problems. For ex-ample, calculating | u + v | could be made a word problem by saying that a bird flew in a straight line in some direction (giving u ) and then in another line (giving v ). How far is the bird from where he started from? Another example is to use vector projections in problems involving force in some direction not parallel to displacement. 1...
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