Phys351-Assignment2

Phys351-Assignment2 - r = 10,θ = π 2,φ = π 36 respectively Determine the shortest distance between these two points if(a one could travel in a

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Assignment #2, Due THIS Thursday. 1. 1.12 – Two points A and B are given by their position vectors ~ r A = 2 ˆ e 1 + 5 ˆ e 2 - 3 ˆ e 3 and ~ r B = - 3 ˆ e 1 + ˆ e 2 + 4 ˆ e 3 . Find (a) the unit vector ˆ e AB that points from point A to point B ; (b) the distance between these two points; (c) the distance from the origin to the midpoint of AB; (d) the point of intersection of the line AB with the ( x = 0) plane. 2. 1.25 – Given ~ r A = 6ˆ e 1 + 2 ˆ e 2 - 3 ˆ e 3 , ~ r B = - 2 ˆ e 1 - 3 ˆ e 2 , and ~ r C = - 4 ˆ e 1 + 6 ˆ e 2 + 5 ˆ e 3 , find (a) the area of the triangle they define, and (b) a unit vector perpendicular to this triangular surface. 3. 1.31 – Find the volume defined by following restrictions on cylindrical coordinates: 4 < ρ < 6, π 6 < φ < π 3 and 2 < z < 5. 4. 1.38 – Points A and B are given by their spherical coordinates r = 10 = π 2 = 0 and
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Unformatted text preview: r = 10 ,θ = π 2 ,φ = π 36 respectively. Determine the shortest distance between these two points if (a) one could travel in a straight line through the sphere, and (b) if you were constrained to move on the spherical surface. 5. Calculate the divergence of the following vector functions: (a) ~v 1 = ( x 1 ) 2 ˆ e 1 + 3( x 1 )( x 3 ) 2 ˆ e 2-2( x 1 )( x 3 ) ˆ e 3 ; (b) ~v 2 = ( x 1 )( x 2 )ˆ e 1 + 2( x 2 )( x 3 ) 2 ˆ e 2 + 3( x 1 )( x 3 ) ˆ e 3 ; 6. Calculate the curl of the following vector functions: (a) ~v 1 = ( x 1 ) 2 ˆ e 1 + 3( x 1 )( x 3 ) 2 ˆ e 2-2( x 1 )( x 3 ) ˆ e 3 ; (b) ~v 2 = ( x 1 )( x 2 )ˆ e 1 + 2( x 2 )( x 3 ) 2 ˆ e 2 + 3( x 1 )( x 3 ) ˆ e 3 ;...
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This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.

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Phys351-Assignment2 - r = 10,θ = π 2,φ = π 36 respectively Determine the shortest distance between these two points if(a one could travel in a

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