MODEL HOME WORK: 1School: LSTCA Department:ECE Name of the faculty member: Mr.MD.IMTIYAZ ANWAR Course No: ECE207Course Title: EMFTClass:B.tech Term: Section: E6912 Batch:09-13Max. Marks: 7 Date of Allotment:18/01/11 Date of Submission:31/01/11

Part AQ1. In Cartesian coordinates, the three corners of a triangle are P1(0,4,4), P2(4,-4,4) and P3(2,2,-4). Find the area of the triangle.

Q2. If the position vectors of points T and S are 3ax- 2ay + az and 4ax + 6ay + 2ax, respectively, find: (a) the coordinates of T and S, (b) the distance vector from T to S, (c) the distance between T and S.

Q3. Show that(A • B)2 + (A X B)2 = (AB)2

Part BQ4. A section of a sphere is described 0 ≤ R ≤ 2, 0 ≤ θ ≤ 900, 300 ≤ φ ≤ 900

Find:(a) The surface area of the spherical section,(b) The enclosed volume.Also sketch the outline of the section.

Q5. Derive the values for the dot product of all unit vectors in Cartesian (ax,ay,az) and spherical (ar,aƟ ,aφ) coordinate systems.

Q6. For the vector field E= 10e-rar – 3z az ; verify the divergence theorem for the cylindrical region enclosed by r = 2, z=0 and z = 4.