## Problem1:Consider the unit sphere centered at the origin and the line with direction (2,1-3a,2-3a) passing through the point (0,a,a). When a=sqrt(2)/2 Find:- The points of intersection between the sphere and the line
- The area of the triangle containning the pts in (1) and the north pole of the sphere.
## Problem2:Find three different vectors in 3D, u,v,w such that the cross product between them is not associative. Solution2## Problem3:Given a line with possition vector u and velocity v, find the coordinates of all the points at a fix distance R from the line. Deduce from there the equation of the cylinder. Solution3## Problem4:Show that the line## Problem5:Find the formula for the angle between a line and a plane and use it to find the angle (in degrees) between the plane x+y-z = -1 and the line y = 1 - 3x on the xy-plane. Solution5## Problem6:Find the cross product and the inner product between the vectors (i+j) and (i-j+k). Solution6## Problem7:Is the distance between to parallel planes, Ax + By + Cz = D1 and Ax + By + Cz = D2 given by |D1-D2| ? If not, what is the correct formula. Find the distance between the planes, x+y+2z=2 and x+y+2z=4. Solution7 |

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Carlos Rodriguez <carlos@math.albany.edu> Last modified: Tue Feb 8 14:07:29 EST 2000