MATH 1320 : Spring 2014
Lab 8
Lab Instructor : Kurt VanNess
Name:
Score:
Write all your solutions on a separate sheet of paper.
1. Given three points P (6, 0, 0), Q(0, 4, 0), R(0, 0, 3), we have a plane P QR:
(a) Find the normal vector to plane P QR.
(b) Use the normal vector to determine the equation for the plane.
(c) What’s the acute angle between plane P QR and the xy-plane?
(d) Use the normal vector to determine the equation of line l that passes through the origin and is
perpendicular to the plane.
(e) Find the intersection point of the line l and plane P QR.
2. Suppose the Earth is a perfect sphere with a radius of R = 6, 367, 444.50m and we ignore altitude for
the time being. Let the North Pole be located at (0, 0, R) and the South Pole at (0, 0, −R) in Cartesian
coordinates. Suppose the Earth is still and doesn’t rotate and the Prime Meridian is in the xz-plane
as shown in the figure.
(a) What is the equation for the surface of the Earth?
(b) Acquaint yourself with the notation of longitude and latitude. We know that some point P near
LCB is a point with the latitude 40◦ 450 5500 N and the longitude 111◦ 500 5800 W . Convert the angles
from degrees, minutes, seconds to radians.
(c) Compute the spherical coordinates of point P .
(d) Convert the spherical coordinates of point P to Cartesian coordinates.
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