|DECEMBER 1998||TIME: 3 HOURS|
|NO CALCULATORS PERMITTED|
|(9)||1.||(a)||Let P,Q,R be the points (1,3,4),(0,-1,2),(-2,1,8).|
|(i)||Find the area of the triangle PQR.|
|(ii)||Find the equation of the plane through P, Qand R.|
|(b)||Find the distance of the point (2,5,-2) from the plane 3x + 2y - 6z = 1.|
|(15)||2.||(a)||Find the equation of the plane containing the line x = 2 + 3t; y = -1 + t; z = t and parallel to the line .|
|(b)||Find the line of intersection of the planes x-y-2z = 4 and 2x + y - z = 2.|
|(c)||Find the distance between the lines (x,y,z) = (1,-2,1) + t(1,0,-3) and .|
|(6)||3.||Find the equation of the surface consisting of all the points that are equidistant from the point (1,0,0) and the plane x = -1. Identify and sketch the surface.|
|(6)||4.||A conic is given by the polar equation
Find the value of
||The radius and height of a cylinder are 20 cm.
and 30 cm. respectively. If they are increased by .04 cm (both radius
and height), what is the volume of the cylinder after the increase?
||Find the tangent plane and normal line to the
x sinz + yez = 4
||Find the rate of change of
f = x2 + 2y2 - z2
+ 4xyz in the direction of
||Classify the critical points of the function
= 2x2 + y2 - xy2 + 4.
||Using the method of Lagrange multipliers, find
the minimum of
f = x2 + y2 + (z-5)2 subject to xy-z = 0.
||Reverse the order of integration and evaluate
||Change the integral to polar coordinates and
||Using spherical coordinates, find the volume of
the solid bounded by the cone
and the plane z =