Homework - 3D Coordinate Systems (Homework)

Consider the point. (3, 5, 6) What is the projection of the point on the xy-plane? ( x, y, z) =( What is the projection of the point on the yz-plane? ( x, y, z ) = What is the projection of the point on the xz-plane? ( x, y, z) = Draw a rectangular box with the origin and (3, 5, 6) as opposite vertices and with its faces parallel to the coordinate planes. Label all vertices of the box. 2 N (6, 0, 0) (6, 5, 0) (0, 0, 6) (5, 0, 6) (6, 0, 3) -(3, 5, 6) (0, 3, 6) (3, 5, 6) y y y 0, 0, 0) (0, 5, 0) (0, 0, 3) 0, 0, 0) (5, 0, 0) (0, 5, 3) (0, 3, Oy (5, 3, 0) x O Find the length of the diagonal of the box. Need Help? Read It Submit AnswerWhat does the equation y = 5 represent in R3? O a point O a line O a plane O a circle What does z = 4 represent? O a point O a line O a plane O a circle What does the pair of equations y = 5, z = 4 represent? In other words, describe the set of points (x, y, z) such that y = 5 and z = 4. O a point O a line O a plane O a circle Illustrate with a sketch. O O Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help Interactive 3D Graph Help 10 N 10 10 10 -10 40 -10 -107 A A Need Help? Read It Submit Answer3. [-/1 Points] DETAILS SCALCET9 12.1.010. Find the distance between the given points. (-6, -4, 1), (3, 2, 5) Need Help? Read It 4. [-/1 Points] DETAILS SCALCET9 12.1.014. Find the distance from (4, -9, 5) to each of the following. (a) the xy-plane (b) the yz-plane (c) the xz-plane (d) the x-axis (e) the y-axis (f) the z-axis Need Help? Read it8. [-/1 Points] DETAILS SCALCET9 12.1.022. Write the equation of the sphere in standard form. 16x7+ 16y + 162 = 96x - 24y - 128 Find its center and radius. center (x, y, z) = radius Need Help? Read It 9. [-/1 Points] DETAILS SCALCET9 12.1.031. Describe in words the region of R* represented by the equation(s) or inequalities. -9Ex= 6 The inequality -9 s x s 6 represents all points on or between the ---Select--- V planes x = -9 and x = Need Help? Read It 10. [-/1 Points] DETAILS SCALCET8 12.1.018. Write the equation of the sphere in standard form. x2 + y2 + 22+ 12x - By + 62+ 57 = 0 Find its center and radius. center (x, y, z)=( radius