Force ‘F’ of intensity 15kN is acting from A (0,-2,4) to B(1,-6,2). Calculate the forcevector.

To calculate the force vector, we first need to find the position vector from point A to point B. The position vector, r, is given by the coordinates of B minus the coordinates of A.

So, r = B - A = (1 - 0, -6 - (-2), 2 - 4) = (1, -4, -2)

The force vector, F, is then given by the intensity of the force times the unit vector in the direction of r. The unit vector, r_hat, is given by r divided by its magnitude.

The magnitude of r, |r|, is given by the square root of the sum of the squares of its components, so |r| = sqrt(1^2 + (-4)^2 + (-2)^2) = sqrt(1 + 16 + 4) = sqrt(21).

So, r_hat = r / |r| = (1/sqrt(21), -4/sqrt(21), -2/sqrt(21)).

Finally, the force vector F is given by the intensity of the force times the unit vector, so F = 15kN * r_hat = (15/sqrt(21) kN, -60/sqrt(21) kN, -30/sqrt(21) kN).