Tutorial -1 For 4th Semester Field Theory- 2140909

TUTORIAL-1

1. Explain dot product and cross product of two vectors.
2. Explain unit vectors of Cartesian, Cylindrical and Spherical co-ordinate system.
3. Explain cylindrical co-ordinate system, differential elements and transformation method from Cylindrical to Cartesian co-ordinate system.
4. Obtain the spherical co-ordinates of (1) 10ā_x at the point P(x= -3, y= 2, z= 4); (2) 10āy at Q (ρ= 5, ɸ= 30°, z= 4); (3) 10āz at R( r= 4,  Ɵ= 110°, ɸ= 120°)
5. Given the points A (x= 2, y= 3, z= 1) and B ( r= 4, Ɵ= 25°, ɸ= 120°). Find (1) The spherical co-ordinate of A  (2) The Cartesian co-ordinate of B (3) The distance from A to B.
6. Transform the vector 4 ā_x-2ā_y-4ā_z into spherical co-ordinates at a point P(x= -2, y= -3, z=4).

Submission   Date : 01/02/16 for Div B     &  03/02/16 for Div A

Prof. P.A. Upadhay /N. N. Makwana