Coordinate systems all centred at the same origin x = y = z = 0: b=-p-20+2, c=37 +30-2φ where i, j, k are cartesian, ρ, φ,2 are cylindrical, and t, θ, φ are spherical. (a) draw a picture with all three vectors. what are their magnitudes? (b) what are the dot products a. b, a c, and b c? (c) what are the cross products a × b, a × c, and b x c?

Asmall electric heater, immersed in 80g of water in a calorimeter of 40j/k raises the temperature from 10.5 degree celsius to 25 degree celsius in 12 minutes. using the same apparatus with 50g of oil instead of water, it is found that the temperature of oil rises from 7 degree celsius to 27 degree celsius in 10 minutes. find specific heat capacity of the oil.