MATH TEXTBOOK PROBLEMS

# MATH TEXTBOOK PROBLEMS - (OORDINATE STCTIO!I I2.I...

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STCTIO!I I2.I Il|REE.t)IMENSIONAL (OORDINATE SYSITMS . 797 l2.l Exercises l. Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward a distance of 3 units. What are the coordinates of your position? l. Sketch the points (0,5,2), (4,0, -I),(2,4,6), and (1, -1,2) on a single set of coordinate axes. 3. Which of the points P(6,2,3), Qes, -L,4), and R(0, 3, 8) is closest to the xz-plane? Which point lies in the yz-plane? 4. What are the projections of the point (2, 3, 5) on the xy-, yz-, and xz-planes? Draw a rectangular box with the origin and (2,3,5) as opposite vertices and with its faces parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box. 5. Describe and sketch the surface in R3 represented by the equa- tionxi-y:2. 6. (a) What does the equation r : 4 represent
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