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Hw12-5 - MATH 1920 Homework 2 Chapter 12.5 8 The normal...

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MATH 1920 Homework 2, Chapter 12.5 8. The normal direction to 3 x + 7 y - 5 z = 21 is h 3 , 7 , - 5 i , then the line that paases through (2 , 4 , 5) and points in that direction is given by x ( t ) = 2 + 3 t , y ( t ) = 4 + 7 t , z ( t ) = 5 - 5 t . 12. The z -axis is given by x ( t ) = 0, y ( t ) = 0, and z ( t ) = t . 22. The plane parallel to the plane 3 x + y + z = 7 also has the form 3 x + y + z = D for some value D . To get what D is, simply plug in the point (1 , - 1 , 3) into the equation, so D = 3 - 1 + 3 = 5. The equation is 3 x + y + z = 5. 28. To find the point of intersection of two lines given by parametric equations, we need to find the parameters t and s for which the corresponding coordinates all match. For the x -coordinate, we have t = 2 s + 2, and for y , - t + 2 = s + 3. These two should suffice to give us the values for t and s . Plugging the first into the second, we have - 2 s - 2 + 2 = s + 3, so s = - 1, hence t = 0. We have to check the z -coordinates agree too. Indeed, t + 1 = 1 and 5 s + 6 = 1. The point that t = 0 and s = - 1 both give is (0 , 2 , 1).
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