The following forces are acting on a particle located at `(2,3,1)`, `bar(F)_(1)=2hat i+3hat j-2hat k,bar(F)_(2)=3hat i+hat j+3hat k,bar(F)_(3)=-5hat i-2hat j+hatk`. Find the torque acting on the particle w.r.t. origin.

If bar(a)=3hat i-3hat j-4hat k, bar(b)=hat i+2hat j+hat k and bar(c)=3hat i-hat j-2hat k , then [bar(a) bar(b) bar(c)] =

A force (hat(i)-2hat(j)+3hat(k)) acts on a particle of position vector (3hat(i)+2hat(j)+hat(k)) . Calculate the torque acting on the particle.

If bar(a)=hat i+2hat j-hat k and bar(b)=3hat i+hat j-5hat k find a unit vector in a direction parallel to vector (bar(a)-bar(b))

Three forces bar(F_(1))=(3hat i+2hat j-hat k)N , bar(F_(2))=(3hat i+4hat j-5hat k)N and bar(F_(3))=A(hat i+hat j-hat k)N act simultaneously on a particle. In order that the particle remains in equilibrium, the value of A should be

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

Following forces start acting on a particle at rest at the origin of the co-ordinate system overset(rarr)F_(1)=-4 hat I -5 hat j +5hat k , overset(rarr)F_(2)=5hat I +8 hat j +6hat k , overset(rarr)F_(3)=-3hat I + 4 hat j - 7 hat k and overset(rarr)F_(4)=2hat i - 3 hat j - 2 hat k then the particle will move

Let bar(u)=hat i+hat j, bar(v)=hat i-hat j,bar(w)=hat i+2hat j+3hat k , n unit vector such that bar(u).bar(n)=0,bar(v).bar(n)=0 then |bar(w).bar(n)| =

Given four forces : vec F_1 = 3 hat i - hat j + 9 hat k vec F_2 = 2 hat i - 2 hat j + 16 hat k vec F_3 = 9 hat i + hat j + 18 hat k vec F_4= hat i + 2 hat j - 18 hat k If all these forces act on a particle at rest at the origin of a coordinate system, then identify the plane in which the particle would begin to move ?

Prove that point hat i+2hat j-3hat k,2hat i-hat j+hat k and 2hat i+5hat j-hat k from a triangle in space.

If bar a=hat i+hat j-4hat k and bar(b)=hat 4i-hat j-2hat k then find (i) a unit vector in the direction of the vector (2bar(a)-bar(b))