Show that `a.(b × c)` is equal in magnitude to the volume of the parallelepiped formed on the three vectors , a, b and c.

Show that veca.(vecbxxvec c) is equal in magnitude to the volume of the parallelopiped formed on the three vectors, veca,vecb and vec c

bar(a),bar(b) and bar( c ) are three non zero, non planar vectors. bar(p)=bar(a)+bar(b)-2bar( c ),bar(q)=3bar(a)-2bar(b)+bar( c ) and bar( r )=bar(a)-4bar(b)+2bar( c ) . The volume of the parallelepiped formed by the vectors bar(a),bar(b) and bar( c ) is V_(1) and the volume of the parallelepiped formed by the vectors bar(p),bar(q) and bar( r ) is V_(2) then V_(2):V_(1) = .............

Show that the magnitude of a vector is equal to the square root of the scalar product of the vector with itself .

Two vectors, both equal in magnitude, have their resultant equal in magnitude of the either. Find the angle between the two vectors.

Read each statement below carefully and state with reasons , if it is true of false : (a) The magnitude of a vector is always a scalar , (b) each component of a vector is always a scalar , (c ) the total path length is always equal to the magnitude of the displacement vector of a particle . (d) the average speed of a either greater or equal to the magnitude of average velocity of the particle over the same interval of time , (e ) Three vectors not lying in a plane can never add up to give a null vector .

Two vectors of equal magnitude 5 unit have an angle 60^0 between them. Find the magnitude of (a) the sum of the vectors and (b) the difference of the vectors. . .

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vector, the angle between these Vector is

Given that vecA+vecB+vecC=0 , out of three vectors two are equal in magnitude and the magnitude of third vector is sqrt2 times that of either of two having equal magnitude. Then angle between vectors are given by

Three concentric spherical metallic shells A, B and C of radii a, b and c (a lt b ltc) have surface charge densities sigma , -sigma and sigma respectively. (i) Find the potential of the three shells A, B and C. (ii) If the shells A and C are at the same potential, obtain the relation between the radii a, b and c.

The sum of three vectors shown in Fig. 2 ( c) . 77. is zero . . (a) What is the magnitude of the vector vec (OB) ? (b) What is the magnitude of the vector vec (OC) ?