Find the work done by a force `barF = 2bari - 3barj +bark` acting on a particle, if the particle is displaced from a point P (-1,2,4) to a point Q(3,1,2) along the line segment PQ.

The work done by the force barF = 2bari-3barj-2bark in moving a particle from (3,-2,5) to (1,-4,3) is

If forces of magnitude 6 and 7 units acting in the direction bari-2barj +2bark and 2bari -3barj -6bark respectively act on particle which is displaced from P (2,-1,-3) to Q(5,-1,1) then the work done by the forces is

The work done by the force barF = abari+barj+bark in moving a particle from (1,1,1) to (2,2,2) along a straight line is 5 units. Then a =

Constant force barF_(1) = 4bari +barj -3bark and barF_(2) = 3bari +barj -bark act on a particle. If the work done where the particle is displaced from A to B, the position vectors of A and B being bari + 2barj +lambda bark and 5bari+4barj+bark respectively is 40 unit then find lambda .

The force barF = 2bari+2barj-bark " acting at " bara =bari-2barj+bark is displaced to a unit distance on Z-axis (OZ=1) direction. The magnitude of the work done by it is

Three forces having magnitudes 5,4 and 3 units act on a particle in the directions 2bari-2barj-bark , bari+2barj+2bark and 2bari+barj-2bark respectively and the particele gets displaced from the point A whose position vector is 6bari-2barj+3bark to the point B whose position vector is 9bari+7barj+5bark then the work done by these forces is

The component of 5bari-3barj+bark " on " 2bari+barj+2bark is

If bara = 3bari-4barj-bark, barb = 2bari + 3barj -6bark are diagonals of a parallelogram, then show that it is a rhombus.

The orthogonal projection vector of bara = 2bari + 3barj+3bark " on " barb=bari-2barj+bark is

A particle is acted upon by constant forces 4bari+barj-3bark and 3bari+barj-bark which displace it from a point bari+2barj+3bark " to the point " 5bari+4barj+bark . The work done in standard unity by the forces is given by