A particle acted on by constant forces` 8hat(i)+2hat(j)-6hat(k)and6hat(i)+2hat(j)-2hat(k)` is displaced from the point `(1,2,3)` to the point `(5,4,1).`
Find the total work done by the forces.

A particle acted on forces vec F_(1)= 3 hati -hat j+ 3 hat k and vecF_(2)= 2 hat i + 3 hat j - 4 hatk , is displaced from the point (3, -2, -1) to the point (1, 5,-2) . Find the total work done by the forces.

A particle is acted upon by the forces vec F_(1)= hati + 2hat j+ 3 hat k , vecF_(2)= 2 hat i + hat j - 3 hatk , vecF_(3) = 3 hat i - 4 hatj + 2 hat k, is displaced from the point (-2, 1, 3) to the point (1, lambda, -2 ) . If the total work done by the forces is 8. Find the value of lambda .

A vector perpendicular to both hat(i) + hat(j) + hat(k) and 2hat(i) + hat(j) + 3hat(k) is,

A force of magnitude 6 units acting parallel to 2hat(i)-2hat(j)+hat(k) displace the point of application from (1,2,3)" to "(5,3,7). Find the work done.

The work done by the force bar(F)=hat(i)+hat(j)+hat(k) acting on a particle, if the particle is displaced from A(3,3,3) to the point B(4,4,4) is …………. units.

Show that the vectors are coplanar hat(i)-2hat(j)+3hat(k),-2hat(i)+3hat(j)-4hat(k),-hat(j)+2hat(k)

Show that the vectors are coplanar 2hat(i)+3hat(j)+hat(k),hat(i)-hat(j),7hat(i)+3hat(j)+2 hat(k)

Forces of magnitude 5sqrt(2)and10sqrt(2) units acting in the directions 3hat(i)+4hat(j)+5kand10hat(j)+6hat(j)-8hat(k), respectively, act on a particle which is displaced from the point with position vector 4hat(i)-3hat(j)-2hat(k) to the with position vector 6hat(i)+hat(j)-3hat(k). Find the work done by the forces.

The vector equation vec(r)=(hat(i)-2hat(j)-hat(k))+t(6hat(j)-hat(k)) represents a straight line passing through the points