# HW 4 - Homework#4 Math 102 Winter 2009 1 Let vectoru =(3 1...

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Unformatted text preview: Homework #4 Math 102, Winter 2009 1. Let vectoru = (3 , 1) and vectorv = ( − 2 , 2). a) Calculate and sketch vectoru + vectorv . b) Calculate and sketch vectoru − vectorv . c) Calculate and sketch − 2 vectoru 2. Text section 3.1, #12 3. Given the initial point P (1 , 3 , 2) and the terminal point Q (4 , 2 , 2) a) Find the components of the vector vectorv having initial point P and ter- minal point Q b) Find the norm of vectorv c) Find a unit vector with the same direction as vectorv 4. Text section 3.3, #3 5. Given vectoru = (3 , 1) and vectora = ( − 4 , 3) a) Find the vector component of vectoru along vectora b) Find the vector component of vectoru orthogonal to vectora c) Find the length of the vector components from a) and b) 6. Given vectoru = (4 , − 1 , 2) vectorv = (3 , 2 , 4) vectorw = (0 , − 1 , 4) a) Is vectorw orthogonal to both vectoru and vectorv ? b) Calculate the scalar triple vectoru · ( vectorv × vectorw ). c) Find the volume of the parallelepiped with sides vectoru , vectorv and vectorw . 1 7. Two planes are defined by the equations 4 x 1 − x 2 + 3 x 3 = 2 2 x 1 + 5 x 2 + x 3 = 3 a) Find the normal vectors for each plane b) Are the planes parallel? Perpendicular? Neither? 8. Text section 3.5, #16 9. Text section 3.5, #41 2 Solutions 1. a) vectoru + vectorv = (3 − 2 , 1 + 2) = (1 , 3) b) vectoru − vectorv = (3 − ( − 2) , 1 − 2)) = (5 , − 1) c) − 2 vectoru = ( − 2(3) , − 2(1)) = ( − 6 , − 2) y x u v u+v a) y x u v b) c) u-v y x u 2u-2u 2. a) x ′ = x − k = 7 − 2 = 5 y ′ = y − l = 5 + 3 = 8 b) x = x ′ + k = − 3 + 2 = − 1 y = y ′ + l...
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HW 4 - Homework#4 Math 102 Winter 2009 1 Let vectoru =(3 1...

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