II. LAB 2: WORKSHEET Solve the following problems, using MATLAB. You will need to submit your 'diary' file or any work by MATLAB as a hardcopy. No softcopy will be accepted. *- Needs to be done by hand 1. Give the distance from point A to point B (a) A = (-2, -15), B = (7,-4) (b) B = (-2,0,7), B= (-3, -5, -9) 2. Find the lengths of the sides of the triangle, then state if it is a right, isosceles, or neither (a) A = (1,-3, -2), B= (5,-1,2), C= (-1, 1,2) (b) A = (5, 1,8), B= (3,5,-5), C= (-7,-8,-1) 3. Determine whether the points lie on a straight line (a) A = (2, -1,3), B= (6, -24,27), C= (-1, 14,15) (b) A = (-1,7,3), B= (3, -5,4), C= (0,1,3) 4. Find an equation of the sphere given the center and the radius, then state the equations if they exists when the sphere intersects with the xy-,xz- and yz-plane (a) * (-5, -6,2), r =5 (b) * (-1,2,4 ), r=4 5. Find an equation of the sphere that passes through the point A and is centered at point O (a) * A= (-3, -5,7), O= (2,4,6) (b) * A = (2,0, -5), O= (9,-4,-1) 6. Construct a regular tetrahedron in the first octant with the two given points, a regular tetrahedron is a 3 dimensional shape whose sides are all equilateral triangles (a) A = (0,0,0), B = (0,0,7) (b) A = (1, 1,0), B = (1,3,0)