Force is a vector
Displacement is a vector.
Work done = scalar product = force . displacement
W = Force * Displacement * cos Ф , where Ф is the angle between force and displacement.
Scalar product is also : Wx = Force in x direction * displacement in x direction
Wy = force in y direction * displacement in y direction
W = Wx + Wy
vector torque = R X F = cross product of displacement (distance) R of vector F force from origin.
Torque = R F sin Ф where Ф is angle between R and F. (from R to F)
Vector product is a vector which has direction = perpendicular to R as well as to F. This is given by thumb rule or curled fingers rule. Toque is perpendicular to plane containing both R & F.
Let i j k be unit vectors along x, y , z axes.
F = Fx i + Fy j
S = x i + y j
W = dot product = F . S = Fx * x + Fy * y
vector product is = F X S = Fx * y k - Fy * x k
i . i = 1 i.j =0 i.k = 0 j.j = 1
i X i =0 j X j = 0