5th - y 2 z = 3 and is perpendicular to the plane x y-2 z =...

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MATH 120 WEEK 5 (RECITATION QUESTIONS) 1. Find an equation of the sphere that passes through the point (4 , 3 , - 1) and has center (3 , 8 , 1). 2. Describe in words the region of < 3 represented by the equation x 2 + y 2 = 1. 3. If v lies in the first quadrant and makes an angle π 3 with the positive x - axis and | v | = 4, find v in component form. 4. Find the angle between a diagonal of a cube and a diagonal of one of its faces. 5. Find the volume of the parallelepiped determined by the vectors a = i + j - k b = i - j + k c = - i + j + k 6. Find an equation of the plane a ) The plane that passes through the point (1 , - 1 , 1) and contains the line with symmetric equations x = 2 y = 3 z . b ) The plane that passes through the line of intersection of the planes x - z = 1 and
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Unformatted text preview: y +2 z = 3 and is perpendicular to the plane x + y-2 z = 1. 7. Find an equation for the plane consisting of all points that are equidistant from the points (-4 , 2 , 1) and (2 ,-4 , 3). 8. Find an equation of the plane with x-intercept a , y-intercept b , and z-intercept c . 9. Find the distance from the point (3 ,-2 , 7) to the given plane 4 x-6 y + z = 5. 10. Find the distance between the given parallel planes. 3 x + 6 y-9 z = 4 , x + 2 y-3 z = 1 11. Find the distance between the skew lines with parametric equations x = 1 + t , y = 1 + 6 t , z = 2 t , and x = 1 + 2 s , y = 5 + 15 s , z =-2 + 6 s . 1...
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