Show thaqt the current I through an area of cross section is given by the scalaer product of two vectors `I=jdelta S` where j and `deltas` and vectors.

Show that the flux delta Phi of electric field E through a small area element delta S is given by delta Phi=E deltaS when delta S = |deltaS|hatn

Give the geometrical meaning of (i) scalar product (ii) cross product of two vectors.

A wire of given material having length I and area of cross-section A has a resistance of 8Omega . What would be the resistance of another wire of the same material having length l/2 and area of cross-section 4A?

Two parallel Co-axial Coils of equal radius R and- numbers of turn N carrying equal currents I in same direction.are separated by a distance | R. Show that the magnetic field intensity B on the axis around the mid point between the coils is uniform over a very small distance as compared to R and is given by- B = (4/5)^(3/2) (mu_0IN)/R

Using vector method find the area of the triangle with two of its adjacent sides given by veca = 4 hati - hatj + 3hatk , vecb = - hati - 2hatj + 4hatk .