Question

Show that torque about the point A(3,-1,3) of a force 4î+2j+k through the point B(5,2,4) is î+2j-8k

Answer 1

we have to show that torque about the point A(3, -1, 3) of a force 4i + 2j + k through the point B(5, 2, 4) is i + 2j - 8k

solution : torque is the cross product of position vector and force.

i.e., τ = r × F

here r = position vector = B(5, 2, 4) - A(3, -1, 3)

= (5 - 3)i + (2 + 1)j + (4 - 3)k

= 2i + 3j + k

F = force vector = 4i + 2j + k

now torque, τ = (2i + 3j + k) × (4i + 2j + k)

= (3 × 1 - 1 × 2)i - (2 × 1 - 1 × 4)j + (2 × 2 - 4 × 3)k

= (3 - 2)i - (2 - 4)j + (4 - 12)k

= i + 2j - 8k [ hence proved ]