In Exercises 1-16. give a geometric description of the set of points in space wh
ID: 2884107 • Letter: I
Question
In Exercises 1-16. give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. I. x = 2, y = 3 2. x = -1. z = 0 3. y = 0. z = 0 4. x = 1, y = 0 5. x^2 + y^2 = 4, z = 0 6. x^2 + y^2 = 4, z = - 2 7. x2 + z^2 = 4. y = 0 8. y^2 + z^2 = 1. x = 0 9. x^2 + y^2 + z^2 = 1. x = 0 10. x^2 + y^2 + z^2 = 25. y = -4 11. x^2 + y^2 + (z + 3)^2 = 25. z = 0 12. x^2 + (y - l)^2 + z^2 - 4, y = 0 13. x^2 + y^2 = 4, z = y 14. x^2 + y^2 + z^2 = 4. y = x 15. y = x^2. z = 0 16. z = y^2, x = 1 In Exercises 1 - 8, let u = (3.-2) and v - (-2, 5). Find the (a) I component form and (b) magnitude (length) of the vector.Explanation / Answer
1. x=2, y=3, This represents a straight line parallel to xy plane and having points of the form (2, 3, z).
2. x=-1, z=0. This represents a straight line parallel to xz plane and having points of the form (-1, y, 0).
3. y=0, z=0, This represents the x-axis.
4. x=1, y=0. This represents a straight line parallel to xy plane and having points of the form (1, 0, z).
5. x^2+y^2=4, z=0.
z=0 represents the xy plane and x^2+y^2=4 represents a circle of radius 2. Thus, together thery represent a circle of radius 2 in xy-plane.
6. x^2+y^2=4, z=-2.
This represent a circle of radius 2 in the plane z=-2.