7/27/2019 Vector Analysis Mid term 2009

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Centre for High energy Physics

B.S 3rdsemester

Computational Physics

Infinite sequence & series

Midterm Examinations (18th

Nov, 2009)

Q.1Derive the parametric equation of projectile motion using vectors? (5)

Q.2Prove the following: (3)

( ) ( ) ( )= ()

Q.3

a) A force of 6 N is applied in the direction of the vector V= 2i +2j-k. Express theforce F as a product of its magnitude and direction. (3)

b) Find the measure of the angles between the diagonals of the rectangle whosevertices are A= (1, 0), B= (0, 3), C= (3, 4) and D= (4, 1). (3)

Q.4

a) Define the equation for plane in space? (2)

b) Find the distance from the point S (1, 1, 5) to the line L: x= 1+t, y= 3- t, z=2t. (3)

Q.5

a) Define cylindrical and spherical co-ordinate system? How are they related to each

other? (3)b) Express the acceleration of particle in cylindrical co-ordinate system? (4)

Q.6

a) Define the Divergence and Curl? Give the Physical interpretation of gradient offunction? (5)

b) Prove the following

(i) Div (curl) = 0 (1)

(ii) Curl (grad) = 0 (1)(iii) Grad ( ) = grad () + grad () (2)

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